A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 1.1 cm. The chocolate used in the bon-bons has a density of 1.28 g\/cm^3 3 . If the chocolate used costs $0.03 per gram, how much would the chocolate for 190 bon-bons cost, to the nearest cent?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine the total cost of the chocolate for 190 bon-bons, we will follow these steps:<\/p>\n\n\n\n The volume of a sphere is given by the formula: [ The mass of an object is calculated using the formula: [ To find the total mass of 190 bon-bons, we multiply the mass of one bon-bon by 190:<\/p>\n\n\n\n [ The cost of the chocolate is $0.03 per gram. So, the total cost for 1355.84 g of chocolate is:<\/p>\n\n\n\n [ The cost of the chocolate for 190 bon-bons is approximately $40.68<\/strong>.<\/p>\n\n\n\n This problem involves calculating the volume, mass, and cost of a set of chocolate bon-bons shaped like spheres. First, we use the formula for the volume of a sphere to find the volume of one bon-bon, given the radius. Then, we use the density to convert the volume into mass. Afterward, we find the total mass of 190 bon-bons. Finally, we multiply the total mass by the cost per gram of chocolate to determine the overall expense. This method allows us to precisely determine the cost based on the given parameters.<\/p>\n","protected":false},"excerpt":{"rendered":" A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 1.1 cm. The chocolate used in the bon-bons has a density of 1.28 g\/cm^3 3 . If the chocolate used costs $0.03 per gram, how much would the chocolate for 190 bon-bons cost, to the nearest cent? The Correct Answer […]<\/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-144083","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144083","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=144083"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144083\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144083"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144083"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Calculate the Volume of One Bon-Bon<\/h3>\n\n\n\n
[
V = \\frac{4}{3} \\pi r^3
]
where ( r ) is the radius of the sphere. Given the radius ( r = 1.1 \\, \\text{cm} ):<\/p>\n\n\n\n
V = \\frac{4}{3} \\pi (1.1)^3 = \\frac{4}{3} \\pi (1.331) \\approx 5.575 \\, \\text{cm}^3
]<\/p>\n\n\n\nStep 2: Calculate the Mass of One Bon-Bon<\/h3>\n\n\n\n
[
\\text{Mass} = \\text{Volume} \\times \\text{Density}
]
The density of the chocolate is 1.28 g\/cm\u00b3. Therefore, the mass of one bon-bon is:<\/p>\n\n\n\n
\\text{Mass} = 5.575 \\, \\text{cm}^3 \\times 1.28 \\, \\text{g\/cm}^3 \\approx 7.136 \\, \\text{g}
]<\/p>\n\n\n\nStep 3: Calculate the Total Mass of 190 Bon-Bons<\/h3>\n\n\n\n
\\text{Total Mass} = 7.136 \\, \\text{g} \\times 190 \\approx 1355.84 \\, \\text{g}
]<\/p>\n\n\n\nStep 4: Calculate the Total Cost of the Chocolate<\/h3>\n\n\n\n
\\text{Total Cost} = 1355.84 \\, \\text{g} \\times 0.03 \\, \\text{dollars\/g} \\approx 40.68 \\, \\text{dollars}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n