Question

A cone with height h and radius r has volume V = 13πr2h. If h is 12 in. and V is equal to 4πx2 – 24πx + 36π, what is the cone’s radius r in terms of x?

Answer 1

r = |x -3|

Explanation:

The cone's volume is ...

`V=(1)/(3)\pi r^2h=(12\pi)/(3)r^2=4\pi r^2`

The version of that containing x is ...

`V=4\pi x^2-24\pi x+36\pi=4\pi (x^2-6x+9)=4\pi (x-3)^2`

Comparing one form to the other, we see that ...

`r^2=(x-3)^2 \qquad\rightarrow\qquad r=|x-3|`

The cone's radius in terms of x is r=|x-3|.