Answer
radius = x
height = (2x+6)
Work Step by Step
Given the volume
$2 \pi x^{3}$ + $12 \pi x^{2}$ + $18 \pi x$
We see that the three terms have a common factor of $2 \pi x^{3}$ so we factor out a $2 \pi x^{3}$.
$2 \pi x(x^{2}$ + 6x + 9)
*** We break of the middle term into two factors that add to give +6 and multiply to give +9. The two numbers are +3 and +3.
$2 \pi x(x^{2}$ + 3x + 3x + 9)
We take the GCD of the first two and the GCD of the last two terms.
$2 \pi x(x(x+3) + 3(x+3))$
We take (x+3) and factor it out which gives us.
$2 \pi x(x+3)(x+3)$
The formula for volume = $ \pi r^{2} h$
So we multiply the to the bracket and get $\pi x^{2} (2x+6)$
According to the formula r= x and h = (2x+6)
