Question

Volume and surface area of a solid sphere are numerically equal. Find it’s radius. Hence find the volume of the cube which just enclose this sphere

Answer 1

Given :  Volume and surface area of a solid sphere are numerically equal.

To find : Radius of Sphere

volume of the cube which just enclose this sphere

Solution:

Radius of Sphere = R

Volume of sphere  = (4/3)πR³

Surface Area of sphere =  4πR²

(4/3)πR³  = 4πR²

=> R = 3

Radius of Sphere = 3 units

Diameter of Sphere = 2 * Radius = 2 * 3 = 6

Cube which will enclose sphere has side = Diameter of sphere  = 6

Volume of cube  = 6³ = 216 cubic units

volume of the cube which just enclose this sphere  = 216 cubic units

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