Question

# If a sphere is inscribed in a cube, find the ratio of the volume of the cube to the volume of the sphere.

Solution

## Let edge of a cube = a  then its volume =a3  ∵ A sphere is inscribed in the cube  ∴ Diameter of sphere =a  and radius =(a2)  ∴Volume of sphere=43πr3 =43π(a2)2 =43π×a38 =πa36  Now ratio between their volumes   =a3:πa36 =6a3:πa3 =6:π

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