Question

A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere? Round your answer to the nearest whole number.

Answer 1

Answer: 113.04 cm^3

Explanation:

The surface area of a cube is:

S = 6*L^2

then:

216 = 6*L^2

216/6 = L^2

L = √(36) = 6

So the length of the side of this square is L = 6cm

Then the diameter of the sphere is also 6 cm, and the radius is half the diameter, so the radius is 3cm.

Now the volume of a sphere is:

V = (4/3)*pi*r^3 = (4/3)*3.14*3^3 = 113.04 cm^3