What is the answer to this?

Question

The surface area S of a sphere of radius r is given by: S=4πr2.

                Solve for r in terms of S.

Answer 1

All problems of this nature are solved the same way and follow 2 rules:

1. Whatever you do on to one side of the equals must be done on the other
2. Anything multiplied by its inverse is equal to 1

With that, you can solve any similar problem.

Suppose

2ab = 3cd²

and you want the expression for a.

First, multiply both sides by the inverse of 2, which is 1/2

(1/2)*(2ab) = (1/2) * (3cd²)

or using associativity

((1/2)*(2))*(ab) = (1/2) * (3cd²)

Because one half times two equals one, you can remove them both from the left side and are left with

ab = (1/2) * (3cd²)

Now apply the inverse trick again with b and you’re left with

a = (1/b) * (1/2) * (3cd²)

Approach your sphere problem the same way. One slight twist is how to handle the square of the radius. You can still think of it like the inverse, though. What’s the ‘inverse’ of raising something to the second power?

Answer 2

if S = 4(pi)r²

Then r² = S/4pi

or r = sqrt(S/4pi)