Question

A sphere fits tightly in cylinder. The surface area of the sphere is 100π square inches. Find Volume of the cylinder.

Give answer in terms of π​

Answer 1

Volume of the cylinder = 250π inch²

Explanation:

Surface area of the cylinder is given by,

Surface area = 4πr²

Here, r = radius of the sphere

Since, surface area = 100π square inches

100π = 4πr²

r² = 25

r = 5

From the picture attached,

Height of the cylinder = diameter of the sphere

= 2(r)

= 2(5)

= 10 inches

Volume of the cylinder is given by,

Volume = πr²h

Here, r = radius of the cylinder

h = height of the cylinder

Therefore, Volume of the cylinder = π(5)²(10)

= 250π square inches