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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# 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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Let r be the radius of the sphere and a be the side of the cube.Surface area of sphere = 4r^{2}Surface area of cube = 6a^{2}Given sphere and cube has same surface area.4r^{2}= 6a^{2}r^{2}/a^{2}= 6/4Volume of the sphere, V_{1 }= (4/3)r^{3}Volume of the cube, V_{2 }= a^{3}Hence proved.