When the height of a cylinder is doubled and its radius is increased by 200%, the cylinder's volume is multiplied by a factor of X. What is the value of X?
The cylinder's original volume is [tex]$\pi r^2h$[/tex]. The new height is 2h and the new radius is [tex]$r+\frac{200}{100}r=3r$[/tex]. That means the new volume is [tex]$\pi (3r)^2(2h)=\pi r^2h(9)(2)$[/tex]. The new volume is the original volume multiplied by a factor of [tex]$\boxed{18}$[/tex].
