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 cylinder radius

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

Step2: Calculate cylinder volume

Volume $V_{\text{cylinder}} = \pi r^2 h = \pi (4)^2 h = 16\pi h$

Step3: Find cone volume

$V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}} = \frac{1}{3} \times 16\pi h = \frac{16}{3}\pi h$

Answer:

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