Answer:
r = |x -3|
Step-by-step explanation:
The cone's volume is ...
[tex]V=\dfrac{1}{3}\pi r^2h=\dfrac{12\pi}{3}r^2=4\pi r^2[/tex]
The version of that containing x is ...
[tex]V=4\pi x^2-24\pi x+36\pi=4\pi (x^2-6x+9)=4\pi (x-3)^2[/tex]
Comparing one form to the other, we see that ...
[tex]r^2=(x-3)^2 \qquad\rightarrow\qquad r=|x-3|[/tex]
The cone's radius in terms of x is r=|x-3|.
