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Deepak Bora
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Asked: 2020-09-25T23:05:40+05:30 In:

A sphere and a cube have the same surface area. Show that the ratio of the volume of the sphere to that of the cube is root 6 : root pi

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This is the Important question of class 10 Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD.
Here A sphere and a cube have the same surface area.
Show that the ratio of the volume of the sphere to that of the cube is √6 :√π
This is the Question Number 09, Exercise 17.3 of M.L Aggarwal.

chapter 17 mensurationicseml aggarwal class 10
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    1 Answer

    1. Let r be the radius of the sphere and a be the side of the cube.

      Surface area of sphere = 4r2

      Surface area of cube = 6a2

      Given sphere and cube has same surface area.

      4r2 = 6a2

      r2/a2 = 6/4

      ML Aggarwal Sol Class 10 Maths chapter 17-7

      Volume of the sphere, V1 = (4/3)r3

      Volume of the cube, V2 = a3

      ML Aggarwal Sol Class 10 Maths chapter 17-8

      Hence proved.

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