Question

find the volume of a cone with a base diameter of 12 yd and a height of 8 yd. write the exact volume in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius of the base

The diameter of the base is 12 yd, so the radius \( r = \frac{12}{2} = 6 \) yd.

Step2: Recall the volume formula for 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.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know \( r = 6 \) yd and \( h = 8 \) yd. Substituting these values, we get:

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The unit of volume is cubic yards, so the volume is \( 96\pi \) cubic yards.

Answer:

\( 96\pi \) cubic yards (or \( 96\pi \text{ yd}^3 \))