Question

find the volume of a cone with a height of 12 ft and a base diameter of 8 ft. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius

The diameter $d = 8$ ft, so the radius $r=\frac{d}{2}=\frac{8}{2}=4$ ft.

Step2: Recall the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step3: Substitute the values

Substitute $r = 4$ ft, $h=12$ ft and $\pi = 3.14$ into the formula: $V=\frac{1}{3}\times3.14\times4^{2}\times12$.
First, calculate $4^{2}=16$. Then $V=\frac{1}{3}\times3.14\times16\times12$.
$\frac{1}{3}\times12 = 4$, so $V=3.14\times16\times4$.
$16\times4 = 64$, and $V=3.14\times64 = 200.96$ ft³.

Answer:

$200.96$ ft³