Question

the volume of the cone shown in the figure below is $\frac{1}{3}$ the volume of the cylinder. in terms of $h$, what is the volume of the cone?

Explanation:

Step1: Find radius of cylinder

Radius $r=\frac{8}{2}=4$.

Step2: Calculate volume of cylinder

Volume of cylinder $V_{cylinder}=\pi r^{2}h=\pi\times4^{2}\times h = 16\pi h$.

Step3: Calculate volume of cone

Since volume of cone $V_{cone}=\frac{1}{3}V_{cylinder}$, then $V_{cone}=\frac{1}{3}\times16\pi h=\frac{16}{3}\pi h$.

Answer:

$\frac{16}{3}\pi h$