Question

What is the surface area of a sphere with a circumference of 50 ft? Round the answer to the nearest tenth.

Answer 1

The surface area of a sphere is:

A=4πr^2

And the circumference of a sphere (or circle) is:

C=2πr

Solving for r, r=C/(2π), and using that for r in the area equation gives you:

A=4π(C/(2π)^2

A=4π(C^2/(4π^2))

A=(4πC^2)/(4π^2)

A=(C^2)/π, since we are told that C=50 ft

A=2500/π ft^2

A≈795.8 ft^2 (to nearest tenth)