Question

the volume of a cone is 36π cubic units. what is the volume of a cylinder with the same radius and the same height?

Explanation:

Step1: Recall volume formulas

The volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$, and the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Relate cone and cylinder volumes

Given the cone and cylinder have the same radius $r$ and height $h$, we can see that $V_{cylinder} = 3V_{cone}$.

Step3: Calculate cylinder volume

We know $V_{cone}=36\pi$. So $V_{cylinder}=3\times36\pi = 108\pi$.

Answer:

$108\pi$