Question

the volume of a cone is 20π cubic meters. what is the volume of a cylinder with the same base and height? the volume of the cylinder is □π cubic meters.

Explanation:

Step1: Recall the volume formulas

The volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\), and the volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\).

Step2: Establish the relationship

If a cone and a cylinder have the same base (\(r\) is the same) and the same height (\(h\) is the same), then \(V_{cylinder} = 3V_{cone}\).

Step3: Calculate the volume of the cylinder

Given \(V_{cone}=20\pi\), then \(V_{cylinder}=3\times20\pi=60\pi\).

Answer:

\(60\pi\)