The height of the cone is 15 centimeters. What is the radius if it has 45pi cubic centimeters

Let's look at the formula for volume of a cone.
V = (1/3)*pi*r^2*h

We know the height and volume, so let's plug those in.

45pi = (1/3)*pi*r^2*15

Simplifying this gives:

45pi = 5pi*r^2

Now we solve for r. Divide both sides by 5pi:

9 = r^2

Take the square root.

r = +/-3

But since length cannot be negative, the answer is simply r = 3.