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Deepak Bora
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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.

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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, V= (4/3)r3

    Volume of the cube, V= a3

    ML Aggarwal Sol Class 10 Maths chapter 17-8

    Hence proved.

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