Question

The volume of the cone is 540. Solve for h, the height of the cone, if the radius is 9.

Answer 1

From the question, we have been given the volume of the cone as 540

Now, volume of a cone is also given by the formula

`V=(1)/(3)\pi r^2h`

Now, the volume is 540 and the radius r is 9. Substituting into the formula, we have

`\begin{gathered} V=(1)/(3)\pi r^2h \\ 540\pi=(1)/(3)*\pi*9^2* h \\ 540\pi=(81\pi h)/(3) \\ 540\pi=27\pi h \\ cancelling\text{ }\pi\text{ at both sides we have } \\ 540=27h \end{gathered}`

Divide both sides by 27, we have

`\begin{gathered} (540)/(27)=(27h)/(27) \\ h=(540)/(27) \\ h=20 \end{gathered}`

Hence the answer is 20