Question

Find the missing measure for a right circular cone given the following information.Find h if r = 5 and V = 100 pi .

Answer 1

The formula for the volume of a cone is

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

Then, we substitute r and V

$100\pi=\frac{\pi\times(5)^2\times h}{3}$

Solve 5^2

$100\pi=\frac{\pi\times25\times h}{3}$

Multiply by 3 on both sides

$\begin{gathered} 3\times100\pi=3\times\frac{25\pi\times h}{3} \\ 300\pi=25\pi\times h \end{gathered}$

Divide by 25pi on both sides

$\begin{gathered} \frac{300\pi}{25\pi}=\frac{25\pi h}{25\pi} \\ h=12 \end{gathered}$

Answer: h = 12