Question

select the correct answer. a cylinder has a volume of 321 cubic units. if a cone has the same height and radius as the cylinder, what is its volume in cubic units? a. 107 cubic units b. 214 cubic units c. 642 cubic units d. 963 cubic units

Explanation:

Step1: Recall volume formulas

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

Step2: Relate cone and cylinder volumes

Since the cone and cylinder have the same radius and height, and $V_{cylinder} = 321$ cubic units, then $V_{cone}=\frac{1}{3}V_{cylinder}$.

Step3: Calculate cone volume

$V_{cone}=\frac{1}{3}\times321 = 107$ cubic units.

Answer:

A. 107 cubic units