Question

1. what is the formula for the volume of a cone?

a. ( 2pi r^{2}h )

b. ( \frac{1}{3}pi r^{2}h )

c. ( \frac{1}{3}pi rh^{2} )

d. ( pi r^{2}h )

Explanation:

Step1: Recall the volume formula derivation

The volume of a cone is related to the volume of a cylinder.

Step2: Volume of cylinder formula

The volume of a cylinder is $V = \pi r^{2}h$.

Step3: Cone - cylinder volume relationship

A cone with the same base radius $r$ and height $h$ has a volume that is one - third of the volume of the cylinder. So, $V_{cone}=\frac{1}{3}V_{cylinder}$.

Step4: Get the cone volume formula

Substituting the cylinder volume formula, we get $V=\frac{1}{3}\pi r^{2}h$.

Answer:

B. $\frac{1}{3}\pi r^{2}h$