answer
the new height is 3 times the original height
explanation
the formula for the volume of a cone is
V = π[tex]\frac{r^2h}{3}[/tex]
given that h is the only thing that changes, π[tex]\frac{r^2}{3}[/tex] would be a constant
dividing both sides by h results in
[tex]\frac{V}{h}[/tex] = π[tex]\frac{r^2}{3}[/tex]
if we triple the volume we now have
[tex]\frac{3V}{h}[/tex]
and since π[tex]\frac{r^2}{3}[/tex] is a constant,
[tex]\frac{V}{h}[/tex] = π[tex]\frac{r^2}{3}[/tex] = [tex]\frac{3V}{xh}[/tex]
[tex]\frac{V}{h}[/tex] = [tex]\frac{3V}{xh}[/tex]
cross multiply
xVh = 3Vh
divide both sides by Vh to get
x = 3
the new height is 3 times the original height
