Question

the volume of a cylinder is 175π cubic units. what is the volume of a cone with the same radius and the same height?

Explanation:

Step1: Recall volume formulas

Volume of cylinder: $V_{cyl} = \pi r^2 h$; Volume of cone: $V_{cone} = \frac{1}{3}\pi r^2 h$

Step2: Relate cone and cylinder volumes

Since $V_{cyl}=175\pi$, substitute into cone formula: $V_{cone}=\frac{1}{3}V_{cyl}$

Step3: Calculate cone volume

$V_{cone}=\frac{1}{3} \times 175\pi$

Answer:

$\frac{175}{3}\pi$ cubic units