Question

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

Answer 1

SOLUTION

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

$V=\frac{1}{3}\pi r^2h$

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

$\begin{gathered} V=\frac{1}{3}\pi r^2h \\ 540\pi=\frac{1}{3}\times\pi\times9^2\times h \\ 540\pi=\frac{81\pi h}{3} \\ 540\pi=27\pi h \\ cancelling\text{ }\pi\text{ at both sides we have } \\ 540=27h \end{gathered}$

Divide both sides by 27, we have

$\begin{gathered} \frac{540}{27}=\frac{27h}{27} \\ h=\frac{540}{27} \\ h=20 \end{gathered}$

Hence the answer is 20