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A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π.
Ans: S.A. of sphere = S.A of cube
4π r2 = 6a2
r = √6a2/4Π
∴ ratio of their volume v1/v 2 = 4/3πy3/a3
On simplifying & substituting, we get √6 : √π
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