4/3πr^3 = 15 in^3

r^3 = 45/4π

Real solution:

r ≈ 1.5299 in

Assuming that have to find r

V = (4/3) π r³

[ 3V / 4π ] = r³

[ 3V / 4π ]^(1/3) = r

I'll guess that you want to find the value of r that makes V=15 in³.

If so, my approach is always to solve in symbols (where possible) to avoid errors writing out long intermediate results. So

V = (4/3) π r³ . . . . given

3V = 4π r³ . . . . multiply by 3 to clear fractions

(3V)/(4π) = r³ . . . . divide by 4π to isolate r

r = ∛[ (3V) / (4π) ] . . . . turn around and take cube roots

Now you're set to find the radius of any sphere, given its volume. For V=15 that's ∛[45 / (4π)]

or about 1.19366 ft. Just over 14 5/16 inches.

If your calculator doesn't have a cube root function, use a 1/3 power instead:

r = [ (3V) / (4π) ] ^ (1/3)