Question

the volume of a cone is 30π cm³. what is the exact volume of a cylinder that has the same radius and height as the cone? enter your answer in the box. v = □ cm³

Explanation:

Step1: Recall the volume formulas

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

Step2: Relate the volumes

Given \( V_{cone} = 30\pi=\frac{1}{3}\pi r^{2}h\). Then \( \pi r^{2}h=3\times30\pi\) (multiply both sides by 3).

Answer:

\(90\pi\)