Question

A cone has a volume of 135π units^3 What is the height of the cone if the diameter of the cone is 18 units long?

Answer 1

Data:

V= 135π cubic units

d= 18 units

h= ?

The volume of a cone is:

$V=\frac{\pi r^2h}{3}$

As you have the diameter, you find the radius:

$\begin{gathered} r=\frac{d}{2} \\ \\ r=\frac{18u}{2}=9u \end{gathered}$

Solve the equation of volume for h:

$\begin{gathered} V=\frac{\pi r^2h}{3} \\ \\ 3V=\pi r^2h \\ \frac{3V}{\pi r^2}=h \end{gathered}$

Then, the height of the cone is: 5 units

$\begin{gathered} h=\frac{3V}{\pi r^2} \\ \\ ^{}h=\frac{3(135\pi u^3)}{\pi(9u^{})^2}=\frac{405\pi u^3}{81\pi u^2}=5u \end{gathered}$