A cone with height h and radius r has volume V = 1/3πr2h. If the cone has a height of 6 in. and volume V = 8πx2 + 24πx + 18π, what is its radius r in terms of x?

C

Step-by-step explanation:

The volume for a cone is given by:

For a given cone with a height of 6 inches, the volume is represented by:

We want to find the radius r in terms of x.

Since the height is 6, this means that:

By substitution:

Divide both sides by 2π:

Factor the right. Notice that we have a perfect square trinomial*:

Factor:

Therefore:

Take the square root of both sides. The radius should be positive, so we only need to consider the positive case:

And our answer is C!

*Note: