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=(\pi r^2h)/(3)`

As you have the diameter, you find the radius:

`\begin{gathered} r=(d)/(2) \\ \\ r=(18u)/(2)=9u \end{gathered}`

Solve the equation of volume for h:

`\begin{gathered} V=(\pi r^2h)/(3) \\ \\ 3V=\pi r^2h \\ (3V)/(\pi r^2)=h \end{gathered}`

Then, the height of the cone is: 5 units

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