Question

1. the formula for the volume of a cone is:

a. ( v=pi r h^{2} )
b. ( v=pi r^{2} h )
c. ( v=\frac{1}{3} pi r^{2} h )
d. ( v=\frac{1}{2} pi r^{2} h )

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is derived from the relationship between a cone and a cylinder with the same base radius \(r\) and height \(h\). A cone has one - third of the volume of a cylinder with the same base and height.
The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\).

Step2: Determine the volume formula of a cone

Since \(V_{cone}=\frac{1}{3}V_{cylinder}\), substituting the formula for the volume of a cylinder, we get \(V_{cone}=\frac{1}{3}\pi r^{2}h\).

Answer:

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