{"id":195400,"date":"2025-02-28T08:21:47","date_gmt":"2025-02-28T08:21:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195400"},"modified":"2025-02-28T08:21:50","modified_gmt":"2025-02-28T08:21:50","slug":"one-cubic-centimeter-of-water-has-a-mass-of-1-00-x-10-3-kg","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/one-cubic-centimeter-of-water-has-a-mass-of-1-00-x-10-3-kg\/","title":{"rendered":"One cubic centimeter of water has a mass of 1.00 x 10-3\u00a0kg"},"content":{"rendered":"\n<p>One cubic centimeter of water has a mass of 1.00 x 10<sup>-3&nbsp;<\/sup>kg. (a) Determine the mass of 1.00 m<sup>3<\/sup>&nbsp;of water. (b) Biological substances are 98% water. Assume that they have the same density as water to estimate the masses of a cell that has a diameter of 1.0%m, a human kidney, and a fly. Model the kidney as a sphere with a radius of 4.0 cm and the fly as a cylinder 4.0 mm long and 2.0 mm in diameter<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1622.png\" alt=\"\" class=\"wp-image-195401\"\/><\/figure>\n\n\n\n<p><strong>(a) Mass of 1.00 m\u00b3 of Water<\/strong><\/p>\n\n\n\n<p>Given that 1 cubic centimeter (1 cm\u00b3) of water has a mass of 1.00 \u00d7 10\u207b\u00b3 kg, we can determine the mass of 1 cubic meter (1 m\u00b3) of water as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Volume Conversion<\/strong>: 1 m\u00b3 equals 1,000,000 cm\u00b3 (since 1 m = 100 cm, thus 1 m\u00b3 = 100\u00b3 cm\u00b3).<\/li>\n\n\n\n<li><strong>Mass Calculation<\/strong>: If 1 cm\u00b3 of water has a mass of 1.00 \u00d7 10\u207b\u00b3 kg, then 1,000,000 cm\u00b3 will have a mass of: [ 1.00 \\times 10^{-3} \\, \\text{kg\/cm}^3 \\times 1,000,000 \\, \\text{cm}^3 = 1,000 \\, \\text{kg} ] Therefore, the mass of 1.00 m\u00b3 of water is <strong>1,000 kg<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p><strong>(b) Estimating Masses of Biological Substances<\/strong><\/p>\n\n\n\n<p>Assuming biological substances are 98% water and have the same density as water, we can estimate the masses of the given entities.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Cell with a Diameter of 1.0 \u00b5m<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Volume Calculation<\/strong>: Modeling the cell as a sphere:\n<ul class=\"wp-block-list\">\n<li>Radius (r): 0.5 \u00b5m = 0.5 \u00d7 10\u207b\u2076 m<\/li>\n\n\n\n<li>Volume (V): [ V = \\frac{4}{3} \\pi r^3 = \\frac{4}{3} \\pi (0.5 \\times 10^{-6} \\, \\text{m})^3 = 5.24 \\times 10^{-19} \\, \\text{m}^3 ]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Mass Calculation<\/strong>: Density of water = 1,000 kg\/m\u00b3.\n<ul class=\"wp-block-list\">\n<li>Mass: [ \\text{Mass} = \\text{Density} \\times \\text{Volume} = 1,000 \\, \\text{kg\/m}^3 \\times 5.24 \\times 10^{-19} \\, \\text{m}^3 = 5.24 \\times 10^{-16} \\, \\text{kg} ]<\/li>\n\n\n\n<li>Adjusting for 98% water content: [ 5.24 \\times 10^{-16} \\, \\text{kg} \\times 0.98 = 5.13 \\times 10^{-16} \\, \\text{kg} ] Thus, the mass of the cell is approximately <strong>5.13 \u00d7 10\u207b\u00b9\u2076 kg<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Human Kidney<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Volume Calculation<\/strong>: Modeling the kidney as a sphere:\n<ul class=\"wp-block-list\">\n<li>Radius (r): 4.0 cm = 0.04 m<\/li>\n\n\n\n<li>Volume (V): [ V = \\frac{4}{3} \\pi r^3 = \\frac{4}{3} \\pi (0.04 \\, \\text{m})^3 = 2.68 \\times 10^{-4} \\, \\text{m}^3 ]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Mass Calculation<\/strong>: Density of water = 1,000 kg\/m\u00b3.\n<ul class=\"wp-block-list\">\n<li>Mass: [ \\text{Mass} = \\text{Density} \\times \\text{Volume} = 1,000 \\, \\text{kg\/m}^3 \\times 2.68 \\times 10^{-4} \\, \\text{m}^3 = 0.268 \\, \\text{kg} ]<\/li>\n\n\n\n<li>Adjusting for 98% water content: [ 0.268 \\, \\text{kg} \\times 0.98 = 0.263 \\, \\text{kg} ] Therefore, the mass of the kidney is approximately <strong>0.263 kg<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Fly<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Volume Calculation<\/strong>: Modeling the fly as a cylinder:\n<ul class=\"wp-block-list\">\n<li>Diameter: 2.0 mm = 0.002 m, thus radius (r) = 0.001 m<\/li>\n\n\n\n<li>Length (h): 4.0 mm = 0.004 m<\/li>\n\n\n\n<li>Volume (V): [ V = \\pi r^2 h = \\pi (0.001 \\, \\text{m})^2 \\times 0.004 \\, \\text{m} = 1.26 \\times 10^{-8} \\, \\text{m}^3 ]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Mass Calculation<\/strong>: Density of water = 1,000 kg\/m\u00b3.\n<ul class=\"wp-block-list\">\n<li>Mass: [ \\text{Mass} = \\text{Density} \\times \\text{Volume} = 1,000 \\, \\text{kg\/m}^3 \\times 1.26 \\times 10^{-8} \\, \\text{m}^3 = 1.26 \\times 10^{-5} \\, \\text{kg} ]<\/li>\n\n\n\n<li>Adjusting for 98% water content: [ 1.26 \\times 10^{-5} \\, \\text{kg} \\times 0.98 = 1.23 \\times 10^{-5} \\, \\text{kg} ] Thus, the mass of the fly is approximately <strong>1.23 \u00d7 10\u207b\u2075 kg<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>These calculations are based on the principle that mass equals density multiplied by volume (Mass = Density \u00d7 Volume). By modeling each biological entity with simple geometric shapes (sphere for the cell and kidney, cylinder for the fly), we can estimate their volumes using standard geometric formulas.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One cubic centimeter of water has a mass of 1.00 x 10-3&nbsp;kg. (a) Determine the mass of 1.00 m3&nbsp;of water. (b) Biological substances are 98% water. Assume that they have the same density as water to estimate the masses of a cell that has a diameter of 1.0%m, a human kidney, and a fly. Model [&hellip;]<\/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-195400","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195400","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=195400"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195400\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}