Volume and Mass of a Standard Gold Bar<\/strong><\/h3>\n\n\n\n
\n\n\n\nPart 1: Calculate the Volume of the Gold Bar<\/strong><\/h3>\n\n\n\nGiven:<\/strong><\/h4>\n\n\n\n\n- Length = 17.78 cm<\/li>\n\n\n\n
- Width = 20.75 cm<\/li>\n\n\n\n
- Height = 4.445 cm<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\nVolume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nVolume=17.78 cm\u00d720.75 cm\u00d74.445 cm\\text{Volume} = 17.78\\ \\text{cm} \\times 20.75\\ \\text{cm} \\times 4.445\\ \\text{cm}Volume=17.78 cm\u00d720.75 cm\u00d74.445 cm<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nVolume=17.78\u00d720.75\u00d74.445=1643.997075 cm3\\text{Volume} = 17.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^3Volume=17.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nAll measurements have 4 significant figures<\/strong>, so:Volume=1644 cm3\\text{Volume} = \\boxed{1644\\ \\text{cm}^3}Volume=1644 cm3\u200b<\/p>\n\n\n\n
\n\n\n\nPart 2: Calculate the Mass of the Gold Bar<\/strong><\/h3>\n\n\n\nGiven:<\/strong><\/h4>\n\n\n\n\n- Volume = 1644 cm\u00b3<\/li>\n\n\n\n
- Density of gold = 19.3 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\nMass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nMass=19.3 g\/cm3\u00d71644 cm3\\text{Mass} = 19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3Mass=19.3 g\/cm3\u00d71644 cm3<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nMass=19.3\u00d71644=31729.2 g\\text{Mass} = 19.3 \\times 1644 = 31729.2\\ \\text{g}Mass=19.3\u00d71644=31729.2 g<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nBoth values have 3 or 4 significant figures; answer should have 3 significant figures<\/strong> (based on the least precise value, 19.3):Mass=3.17\u00d7104 g\\text{Mass} = \\boxed{3.17 \\times 10^4\\ \\text{g}}Mass=3.17\u00d7104 g\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation (Textbook-Style, ~300 Words)<\/strong><\/h3>\n\n\n\nTo determine the volume<\/strong> of a standard gold bar, we multiply its three dimensions (length, width, and height), each given in centimeters<\/strong>, because volume in cubic centimeters is calculated from multiplying three linear measurements in centimeters. The formula for volume of a rectangular solid is:Volume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\nUsing the values provided\u201417.78 cm (length), 20.75 cm (width), and 4.445 cm (height)\u2014the product of these three gives the volume:17.78\u00d720.75\u00d74.445=1643.997075 cm317.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^317.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
When rounding for significant figures, we consider the measurement with the fewest significant figures<\/strong>, which in this case is four, so the final volume is rounded to 1644 cm\u00b3<\/strong>.<\/p>\n\n\n\nNext, using the density formula<\/strong>, which relates mass to volume through:Mass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\nand the known density of gold (19.3 g\/cm\u00b3), we multiply this by the volume to get:19.3 g\/cm3\u00d71644 cm3=31729.2 g19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3 = 31729.2\\ \\text{g}19.3 g\/cm3\u00d71644 cm3=31729.2 g<\/p>\n\n\n\n
The mass is then rounded to 3 significant figures<\/strong> because 19.3 has 3 significant figures. Therefore, the mass of one standard gold bar is 3.17 \u00d7 10\u2074 grams<\/strong>, or 31.7 kilograms<\/strong>, since 1,000 grams = 1 kilogram. This calculation is important in finance and science, where precision matters in valuing precious metals.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-226.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"According to the US Mint, the standard gold bar is 17.78 cm by 20.75 cm by 4.445 cm. Calculate the volume of the gold bar in units of cubic centimeters. Write Equation Rearrange Equation Substitute Numbers with Units Calculate Final Answer with Correct Number, Units; SF The density of pure gold is 19.3 g\/cm^3. Use […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233389","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233389"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Given:<\/strong><\/h4>\n\n\n\n\n- Length = 17.78 cm<\/li>\n\n\n\n
- Width = 20.75 cm<\/li>\n\n\n\n
- Height = 4.445 cm<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\nVolume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nVolume=17.78 cm\u00d720.75 cm\u00d74.445 cm\\text{Volume} = 17.78\\ \\text{cm} \\times 20.75\\ \\text{cm} \\times 4.445\\ \\text{cm}Volume=17.78 cm\u00d720.75 cm\u00d74.445 cm<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nVolume=17.78\u00d720.75\u00d74.445=1643.997075 cm3\\text{Volume} = 17.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^3Volume=17.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nAll measurements have 4 significant figures<\/strong>, so:Volume=1644 cm3\\text{Volume} = \\boxed{1644\\ \\text{cm}^3}Volume=1644 cm3\u200b<\/p>\n\n\n\n
\n\n\n\nPart 2: Calculate the Mass of the Gold Bar<\/strong><\/h3>\n\n\n\nGiven:<\/strong><\/h4>\n\n\n\n\n- Volume = 1644 cm\u00b3<\/li>\n\n\n\n
- Density of gold = 19.3 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\nMass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nMass=19.3 g\/cm3\u00d71644 cm3\\text{Mass} = 19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3Mass=19.3 g\/cm3\u00d71644 cm3<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nMass=19.3\u00d71644=31729.2 g\\text{Mass} = 19.3 \\times 1644 = 31729.2\\ \\text{g}Mass=19.3\u00d71644=31729.2 g<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nBoth values have 3 or 4 significant figures; answer should have 3 significant figures<\/strong> (based on the least precise value, 19.3):Mass=3.17\u00d7104 g\\text{Mass} = \\boxed{3.17 \\times 10^4\\ \\text{g}}Mass=3.17\u00d7104 g\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation (Textbook-Style, ~300 Words)<\/strong><\/h3>\n\n\n\nTo determine the volume<\/strong> of a standard gold bar, we multiply its three dimensions (length, width, and height), each given in centimeters<\/strong>, because volume in cubic centimeters is calculated from multiplying three linear measurements in centimeters. The formula for volume of a rectangular solid is:Volume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\nUsing the values provided\u201417.78 cm (length), 20.75 cm (width), and 4.445 cm (height)\u2014the product of these three gives the volume:17.78\u00d720.75\u00d74.445=1643.997075 cm317.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^317.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
When rounding for significant figures, we consider the measurement with the fewest significant figures<\/strong>, which in this case is four, so the final volume is rounded to 1644 cm\u00b3<\/strong>.<\/p>\n\n\n\nNext, using the density formula<\/strong>, which relates mass to volume through:Mass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\nand the known density of gold (19.3 g\/cm\u00b3), we multiply this by the volume to get:19.3 g\/cm3\u00d71644 cm3=31729.2 g19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3 = 31729.2\\ \\text{g}19.3 g\/cm3\u00d71644 cm3=31729.2 g<\/p>\n\n\n\n
The mass is then rounded to 3 significant figures<\/strong> because 19.3 has 3 significant figures. Therefore, the mass of one standard gold bar is 3.17 \u00d7 10\u2074 grams<\/strong>, or 31.7 kilograms<\/strong>, since 1,000 grams = 1 kilogram. This calculation is important in finance and science, where precision matters in valuing precious metals.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"According to the US Mint, the standard gold bar is 17.78 cm by 20.75 cm by 4.445 cm. Calculate the volume of the gold bar in units of cubic centimeters. Write Equation Rearrange Equation Substitute Numbers with Units Calculate Final Answer with Correct Number, Units; SF The density of pure gold is 19.3 g\/cm^3. Use […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233389","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233389"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
Step 1: Write the Equation<\/strong><\/h4>\n\n\n\nVolume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nVolume=17.78 cm\u00d720.75 cm\u00d74.445 cm\\text{Volume} = 17.78\\ \\text{cm} \\times 20.75\\ \\text{cm} \\times 4.445\\ \\text{cm}Volume=17.78 cm\u00d720.75 cm\u00d74.445 cm<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nVolume=17.78\u00d720.75\u00d74.445=1643.997075 cm3\\text{Volume} = 17.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^3Volume=17.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nAll measurements have 4 significant figures<\/strong>, so:Volume=1644 cm3\\text{Volume} = \\boxed{1644\\ \\text{cm}^3}Volume=1644 cm3\u200b<\/p>\n\n\n\n
\n\n\n\nPart 2: Calculate the Mass of the Gold Bar<\/strong><\/h3>\n\n\n\nGiven:<\/strong><\/h4>\n\n\n\n\n- Volume = 1644 cm\u00b3<\/li>\n\n\n\n
- Density of gold = 19.3 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\nMass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nMass=19.3 g\/cm3\u00d71644 cm3\\text{Mass} = 19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3Mass=19.3 g\/cm3\u00d71644 cm3<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nMass=19.3\u00d71644=31729.2 g\\text{Mass} = 19.3 \\times 1644 = 31729.2\\ \\text{g}Mass=19.3\u00d71644=31729.2 g<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nBoth values have 3 or 4 significant figures; answer should have 3 significant figures<\/strong> (based on the least precise value, 19.3):Mass=3.17\u00d7104 g\\text{Mass} = \\boxed{3.17 \\times 10^4\\ \\text{g}}Mass=3.17\u00d7104 g\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation (Textbook-Style, ~300 Words)<\/strong><\/h3>\n\n\n\nTo determine the volume<\/strong> of a standard gold bar, we multiply its three dimensions (length, width, and height), each given in centimeters<\/strong>, because volume in cubic centimeters is calculated from multiplying three linear measurements in centimeters. The formula for volume of a rectangular solid is:Volume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\nUsing the values provided\u201417.78 cm (length), 20.75 cm (width), and 4.445 cm (height)\u2014the product of these three gives the volume:17.78\u00d720.75\u00d74.445=1643.997075 cm317.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^317.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
When rounding for significant figures, we consider the measurement with the fewest significant figures<\/strong>, which in this case is four, so the final volume is rounded to 1644 cm\u00b3<\/strong>.<\/p>\n\n\n\nNext, using the density formula<\/strong>, which relates mass to volume through:Mass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\nand the known density of gold (19.3 g\/cm\u00b3), we multiply this by the volume to get:19.3 g\/cm3\u00d71644 cm3=31729.2 g19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3 = 31729.2\\ \\text{g}19.3 g\/cm3\u00d71644 cm3=31729.2 g<\/p>\n\n\n\n
The mass is then rounded to 3 significant figures<\/strong> because 19.3 has 3 significant figures. Therefore, the mass of one standard gold bar is 3.17 \u00d7 10\u2074 grams<\/strong>, or 31.7 kilograms<\/strong>, since 1,000 grams = 1 kilogram. This calculation is important in finance and science, where precision matters in valuing precious metals.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"According to the US Mint, the standard gold bar is 17.78 cm by 20.75 cm by 4.445 cm. Calculate the volume of the gold bar in units of cubic centimeters. Write Equation Rearrange Equation Substitute Numbers with Units Calculate Final Answer with Correct Number, Units; SF The density of pure gold is 19.3 g\/cm^3. Use […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233389","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233389"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Volume=17.78 cm\u00d720.75 cm\u00d74.445 cm\\text{Volume} = 17.78\\ \\text{cm} \\times 20.75\\ \\text{cm} \\times 4.445\\ \\text{cm}Volume=17.78 cm\u00d720.75 cm\u00d74.445 cm<\/p>\n\n\n\n
\n\n\n\n
Step 3: Calculate<\/strong><\/h4>\n\n\n\nVolume=17.78\u00d720.75\u00d74.445=1643.997075 cm3\\text{Volume} = 17.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^3Volume=17.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nAll measurements have 4 significant figures<\/strong>, so:Volume=1644 cm3\\text{Volume} = \\boxed{1644\\ \\text{cm}^3}Volume=1644 cm3\u200b<\/p>\n\n\n\n
\n\n\n\nPart 2: Calculate the Mass of the Gold Bar<\/strong><\/h3>\n\n\n\nGiven:<\/strong><\/h4>\n\n\n\n\n- Volume = 1644 cm\u00b3<\/li>\n\n\n\n
- Density of gold = 19.3 g\/cm\u00b3<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\nMass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\nMass=19.3 g\/cm3\u00d71644 cm3\\text{Mass} = 19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3Mass=19.3 g\/cm3\u00d71644 cm3<\/p>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\nMass=19.3\u00d71644=31729.2 g\\text{Mass} = 19.3 \\times 1644 = 31729.2\\ \\text{g}Mass=19.3\u00d71644=31729.2 g<\/p>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\nBoth values have 3 or 4 significant figures; answer should have 3 significant figures<\/strong> (based on the least precise value, 19.3):Mass=3.17\u00d7104 g\\text{Mass} = \\boxed{3.17 \\times 10^4\\ \\text{g}}Mass=3.17\u00d7104 g\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation (Textbook-Style, ~300 Words)<\/strong><\/h3>\n\n\n\nTo determine the volume<\/strong> of a standard gold bar, we multiply its three dimensions (length, width, and height), each given in centimeters<\/strong>, because volume in cubic centimeters is calculated from multiplying three linear measurements in centimeters. The formula for volume of a rectangular solid is:Volume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\nUsing the values provided\u201417.78 cm (length), 20.75 cm (width), and 4.445 cm (height)\u2014the product of these three gives the volume:17.78\u00d720.75\u00d74.445=1643.997075 cm317.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^317.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n
When rounding for significant figures, we consider the measurement with the fewest significant figures<\/strong>, which in this case is four, so the final volume is rounded to 1644 cm\u00b3<\/strong>.<\/p>\n\n\n\nNext, using the density formula<\/strong>, which relates mass to volume through:Mass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\nand the known density of gold (19.3 g\/cm\u00b3), we multiply this by the volume to get:19.3 g\/cm3\u00d71644 cm3=31729.2 g19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3 = 31729.2\\ \\text{g}19.3 g\/cm3\u00d71644 cm3=31729.2 g<\/p>\n\n\n\n
The mass is then rounded to 3 significant figures<\/strong> because 19.3 has 3 significant figures. Therefore, the mass of one standard gold bar is 3.17 \u00d7 10\u2074 grams<\/strong>, or 31.7 kilograms<\/strong>, since 1,000 grams = 1 kilogram. This calculation is important in finance and science, where precision matters in valuing precious metals.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"According to the US Mint, the standard gold bar is 17.78 cm by 20.75 cm by 4.445 cm. Calculate the volume of the gold bar in units of cubic centimeters. Write Equation Rearrange Equation Substitute Numbers with Units Calculate Final Answer with Correct Number, Units; SF The density of pure gold is 19.3 g\/cm^3. Use […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233389","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233389"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
All measurements have 4 significant figures<\/strong>, so:Volume=1644 cm3\\text{Volume} = \\boxed{1644\\ \\text{cm}^3}Volume=1644 cm3\u200b<\/p>\n\n\n\n Mass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\n Mass=19.3 g\/cm3\u00d71644 cm3\\text{Mass} = 19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3Mass=19.3 g\/cm3\u00d71644 cm3<\/p>\n\n\n\n Mass=19.3\u00d71644=31729.2 g\\text{Mass} = 19.3 \\times 1644 = 31729.2\\ \\text{g}Mass=19.3\u00d71644=31729.2 g<\/p>\n\n\n\n Both values have 3 or 4 significant figures; answer should have 3 significant figures<\/strong> (based on the least precise value, 19.3):Mass=3.17\u00d7104 g\\text{Mass} = \\boxed{3.17 \\times 10^4\\ \\text{g}}Mass=3.17\u00d7104 g\u200b<\/p>\n\n\n\n To determine the volume<\/strong> of a standard gold bar, we multiply its three dimensions (length, width, and height), each given in centimeters<\/strong>, because volume in cubic centimeters is calculated from multiplying three linear measurements in centimeters. The formula for volume of a rectangular solid is:Volume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}Volume=Length\u00d7Width\u00d7Height<\/p>\n\n\n\n Using the values provided\u201417.78 cm (length), 20.75 cm (width), and 4.445 cm (height)\u2014the product of these three gives the volume:17.78\u00d720.75\u00d74.445=1643.997075 cm317.78 \\times 20.75 \\times 4.445 = 1643.997075\\ \\text{cm}^317.78\u00d720.75\u00d74.445=1643.997075 cm3<\/p>\n\n\n\n When rounding for significant figures, we consider the measurement with the fewest significant figures<\/strong>, which in this case is four, so the final volume is rounded to 1644 cm\u00b3<\/strong>.<\/p>\n\n\n\n Next, using the density formula<\/strong>, which relates mass to volume through:Mass=Density\u00d7Volume\\text{Mass} = \\text{Density} \\times \\text{Volume}Mass=Density\u00d7Volume<\/p>\n\n\n\n and the known density of gold (19.3 g\/cm\u00b3), we multiply this by the volume to get:19.3 g\/cm3\u00d71644 cm3=31729.2 g19.3\\ \\text{g\/cm}^3 \\times 1644\\ \\text{cm}^3 = 31729.2\\ \\text{g}19.3 g\/cm3\u00d71644 cm3=31729.2 g<\/p>\n\n\n\n The mass is then rounded to 3 significant figures<\/strong> because 19.3 has 3 significant figures. Therefore, the mass of one standard gold bar is 3.17 \u00d7 10\u2074 grams<\/strong>, or 31.7 kilograms<\/strong>, since 1,000 grams = 1 kilogram. This calculation is important in finance and science, where precision matters in valuing precious metals.<\/p>\n\n\n\n According to the US Mint, the standard gold bar is 17.78 cm by 20.75 cm by 4.445 cm. Calculate the volume of the gold bar in units of cubic centimeters. Write Equation Rearrange Equation Substitute Numbers with Units Calculate Final Answer with Correct Number, Units; SF The density of pure gold is 19.3 g\/cm^3. Use […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233389","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233389"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233389\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nPart 2: Calculate the Mass of the Gold Bar<\/strong><\/h3>\n\n\n\n
Given:<\/strong><\/h4>\n\n\n\n
\n
\n\n\n\nStep 1: Write the Equation<\/strong><\/h4>\n\n\n\n
\n\n\n\nStep 2: Substitute the Numbers (with Units)<\/strong><\/h4>\n\n\n\n
\n\n\n\nStep 3: Calculate<\/strong><\/h4>\n\n\n\n
\n\n\n\nStep 4: Round to Correct Significant Figures<\/strong><\/h4>\n\n\n\n
\n\n\n\nExplanation (Textbook-Style, ~300 Words)<\/strong><\/h3>\n\n\n\n
<\/figure>\n","protected":false},"excerpt":{"rendered":"