Question

find the volume of a cone with a base radius of 4 yd and a height of 6 yd. 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 formula for the volume \( V \) of a cone is \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Identify the values of \( r \) and \( h \)

From the problem, the radius \( r = 4\) yd and the height \( h=6\) yd.

Step3: Substitute the values into the formula

Substitute \( r = 4 \) and \( h = 6 \) into the formula \( V=\frac{1}{3}\pi r^{2}h \):

$$
LATEXBLOCK0
$$

The unit of volume for a three - dimensional object with linear units in yards is cubic yards (\( \text{yd}^3 \)).

Answer:

\( 32\pi \) cubic yards or \( 32\pi\ \text{yd}^3 \)