Question

the formula for the volume of a cone is:
a. $v = \frac{1}{3}\pi r^{2}h$
b. $v = \frac{1}{2}\pi r^{2}h$
c. $v = \pi rh^{2}$
d. $v = \pi r^{2}h$

Explanation:

Step1: Recall the volume formula of a cone

The volume of a cone is related to the volume of a cylinder with the same base radius \(r\) and height \(h\).

Step2: Relationship between cone and cylinder volume

The volume of a cylinder is \(V_{cylinder}=\pi r^{2}h\). A cone has one - third of the volume of a cylinder with the same base and height. So \(V_{cone}=\frac{1}{3}\pi r^{2}h\)

Answer:

A. \( V = \frac{1}{3}\pi r^{2}h\)