Question

the volume of a cylinder is $40\\ ft^{3}$. which expression represents the volume of a cone with the same base and height as the cylinder?

$\frac{1}{3}(40)\\ ft^{3}$

$\frac{1}{3}(40^{2})\\ ft^{3}$

$3(40)\\ ft^{3}$

$3(\frac{1}{40})\\ ft^{3}$

Explanation:

Step1: Recall volume formulas

Volume of cylinder \(V_{cylinder}=\pi r^{2}h\), volume of cone \(V_{cone}=\frac{1}{3}\pi r^{2}h\).

Step2: Compare volumes

If \(V_{cylinder}=\pi r^{2}h = 40\) (same base \(r\) and height \(h\)), then \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Answer:

\(\frac{1}{3}(40)\text{ ft}^3\)