Question

the volume of a cylinder is approximately 72 ft³. which is the best approximation of the volume of a cone with the same base and height as the cylinder? 216 ft³ 216π ft³ 24π ft³ 24 ft³

Explanation:

Step1: Recall the volume formulas

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\), and the volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). If a cone has the same base (\(r\)) and height (\(h\)) as a cylinder, then \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Step2: Substitute the given volume of the cylinder

Given \(V_{cylinder} = 72\mathrm{ft}^{3}\). Substitute into the formula \(V_{cone}=\frac{1}{3}V_{cylinder}\). So \(V_{cone}=\frac{1}{3}\times72\).

$$ \frac{1}{3}\times72=\frac{72}{3}=24 $$

Answer:

\(24\mathrm{ft}^{3}\)