Question

find the volume of a cone with a base radius of 3 in and a height of 10 in. write the exact volume in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Substitute the given values into the formula

We are given that the radius \( r = 3 \) in and the height \( h = 10 \) in. Substituting these values into the formula, we get:
\( V = \frac{1}{3}\pi (3)^2 (10) \)

Step3: Simplify the expression

First, calculate \( (3)^2 = 9 \). Then, multiply \( \frac{1}{3} \times 9 \times 10 \).
\( \frac{1}{3} \times 9 = 3 \), and then \( 3 \times 10 = 30 \). So the volume \( V = 30\pi \) cubic inches.

Answer:

\( 30\pi \) cubic inches (or \( 30\pi \) in³)