{"id":224046,"date":"2025-06-02T16:30:30","date_gmt":"2025-06-02T16:30:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224046"},"modified":"2025-06-02T16:30:33","modified_gmt":"2025-06-02T16:30:33","slug":"a-chemist-has-an-empty-cylinder-with-a-height-of-30-cm-and-a-cone-shaped-flask","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/a-chemist-has-an-empty-cylinder-with-a-height-of-30-cm-and-a-cone-shaped-flask\/","title":{"rendered":"A chemist has an empty cylinder with a height of 30 cm and a cone-shaped flask"},"content":{"rendered":"\n

A chemist has an empty cylinder with a height of 30 cm and a cone-shaped flask. The flask has the same height and a base that is the same size as the cylinder’s. The flask is filled with water, which she pours into the cylinder. To what height does the water fill the cylinder? 30 cm 15 cm 10 cm 20 cm<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer: 10 cm<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

We are given:<\/p>\n\n\n\n

    \n
  • A cylinder<\/strong> and a cone-shaped flask<\/strong> that have:\n
      \n
    • The same height<\/strong>: 30 cm<\/li>\n\n\n\n
    • The same base area<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • The cone-shaped flask is filled with water and emptied into the cylinder.<\/li>\n\n\n\n
    • We need to find to what height<\/strong> the water will fill the cylinder<\/strong>.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Step-by-step Reasoning:<\/h3>\n\n\n\n

      Step 1: Use volume formulas<\/h4>\n\n\n\n

      The volume of a cylinder<\/strong> is given by: Vcylinder=\u03c0r2hV_{\\text{cylinder}} = \\pi r^2 h<\/p>\n\n\n\n

      The volume of a cone<\/strong> is: Vcone=13\u03c0r2hV_{\\text{cone}} = \\frac{1}{3} \\pi r^2 h<\/p>\n\n\n\n

      Because the cone and the cylinder have the same radius<\/strong> and same height<\/strong>, we can directly compare volumes.<\/p>\n\n\n\n

      Let\u2019s suppose the radius is rr and the height is 3030 cm.<\/p>\n\n\n\n

      Then:<\/p>\n\n\n\n

        \n
      • Volume of the cylinder<\/strong>: \u03c0r2\u00d730\\pi r^2 \\times 30<\/li>\n\n\n\n
      • Volume of the cone<\/strong>: 13\u03c0r2\u00d730=\u03c0r2\u00d710\\frac{1}{3} \\pi r^2 \\times 30 = \\pi r^2 \\times 10<\/li>\n<\/ul>\n\n\n\n

        So, the volume of the cone is 1\/3<\/strong> the volume of the cylinder.<\/p>\n\n\n\n

        \n\n\n\n

        Step 2: Volume of water in the cylinder<\/h4>\n\n\n\n

        The entire volume of the cone-shaped flask<\/strong> (water) is poured into the empty cylinder.<\/p>\n\n\n\n

        So, water fills: 13 of the cylinder\u2019s height\\frac{1}{3} \\text{ of the cylinder\u2019s height} Height filled=13\u00d730 cm=10 cm\\text{Height filled} = \\frac{1}{3} \\times 30 \\text{ cm} = 10 \\text{ cm}<\/p>\n\n\n\n

        \n\n\n\n

        Final Answer:<\/h3>\n\n\n\n

        10 cm<\/strong><\/p>\n\n\n\n

        This means the cylinder will be filled to a height of 10 cm<\/strong> with the water from the cone-shaped flask.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        A chemist has an empty cylinder with a height of 30 cm and a cone-shaped flask. The flask has the same height and a base that is the same size as the cylinder’s. The flask is filled with water, which she pours into the cylinder. To what height does the water fill the cylinder? 30 […]<\/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-224046","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224046","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=224046"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224046\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}