Question

A sphere and a cube have equal surface areas. The length of one edge of the cube is 1.11 meters. What is the radius of the sphere?

Answer 1

0.767 m

Explanation:

The area of a cube of edge length s is given by ...

A = 6s^2

The area of a sphere of radius r is given by ...

A = 4πr^2

When these two are equal, we have ...

6s^2 = 4πr^2

r^2 = 6s^2/(4π)

r = s·√(3/(2π)) ≈ s·0.690988

The radius of the sphere is about ...

r ≈ 0.690899×1.11 m

r ≈ 0.767 m . . . . approximate sphere radius