A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 2 cm. The chocolate used in the bon-bons has a density of 1.31 g\/cm\u00ba. If the chocolate used costs $0.06 per gram, how much would the chocolate for 140 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 find the cost of the chocolate used in 140 bon-bons, we need to first calculate the volume of chocolate used for one bon-bon, then its mass, and finally determine the total cost for 140 bon-bons.<\/p>\n\n\n\n Since the bon-bons are spherical, the formula for the volume of a sphere is: Substitute the radius into the formula: So, the volume of one bon-bon is approximately 33.51 cubic centimeters.<\/p>\n\n\n\n The mass of the chocolate in one bon-bon can be calculated using the density of the chocolate. The formula is: [ So, the mass of chocolate in one bon-bon is approximately 43.89 grams.<\/p>\n\n\n\n Now, we calculate the cost of the chocolate in one bon-bon. The cost is $0.06 per gram: So, the cost of chocolate for one bon-bon is approximately $2.63.<\/p>\n\n\n\n To find the total cost for 140 bon-bons, we multiply the cost for one bon-bon by 140: Thus, the total cost of chocolate for 140 bon-bons is approximately $368.20<\/strong>.<\/p>\n\n\n\n The total cost for the chocolate used in 140 bon-bons is $368.20<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 2 cm. The chocolate used in the bon-bons has a density of 1.31 g\/cm\u00ba. If the chocolate used costs $0.06 per gram, how much would the chocolate for 140 bon-bons cost, to the nearest cent? The Correct Answer and Explanation […]<\/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-179689","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179689","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=179689"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179689\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179689"}],"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. For this problem, ( r = 2 \\, \\text{cm} ).<\/p>\n\n\n\n
[
V = \\frac{4}{3} \\pi (2)^3 = \\frac{4}{3} \\pi \\times 8 = \\frac{32}{3} \\pi \\approx 33.51 \\, \\text{cm}^3
]<\/p>\n\n\n\nStep 2: Calculate the Mass of Chocolate in One Bon-Bon<\/h3>\n\n\n\n
[
\\text{mass} = \\text{density} \\times \\text{volume}
]
The density of the chocolate is 1.31 g\/cm\u00b3, and the volume is 33.51 cm\u00b3.<\/p>\n\n\n\n
\\text{mass} = 1.31 \\, \\text{g\/cm}^3 \\times 33.51 \\, \\text{cm}^3 = 43.89 \\, \\text{g}
]<\/p>\n\n\n\nStep 3: Calculate the Cost of Chocolate for One Bon-Bon<\/h3>\n\n\n\n
[
\\text{cost per bon-bon} = 43.89 \\, \\text{g} \\times 0.06 \\, \\text{\\$\/g} = 2.63 \\, \\text{\\$}
]<\/p>\n\n\n\nStep 4: Calculate the Total Cost for 140 Bon-Bons<\/h3>\n\n\n\n
[
\\text{total cost} = 2.63 \\, \\text{\\$} \\times 140 = 368.20 \\, \\text{\\$}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n