Question

the volume of a cone is $36\pi\text{ in}^3$. what is the volume of a cylinder with the same base and height as the cone? $108\pi\text{ in}^3$ $72\pi\text{ in}^3$ $12\pi\text{ in}^3$ $36\pi\text{ in}^3$

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 \(V_{cylinder}=\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height.

Step2: Establish the relationship between the volumes

If a cylinder and a cone 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 \(V_{cone} = 36\pi\space in^{3}\), substitute into the relationship \(V_{cylinder}=3\times36\pi\).

$$V_{cylinder}=108\pi\space in^{3}$$

Answer:

\(108\pi\space in^{3}\)