Question

find the volume of a cone with a height of 12 m and a base diameter of 12 m. 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 of the base

The diameter $d = 12$ m, and the radius $r=\frac{d}{2}$. So $r=\frac{12}{2}=6$ m.

Step2: Use the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 6$ m, $h = 12$ m and $\pi=3.14$ into the formula. $V=\frac{1}{3}\times3.14\times6^{2}\times12$.
First, calculate $6^{2}=36$. Then $V=\frac{1}{3}\times3.14\times36\times12$.
$\frac{1}{3}\times36 = 12$, so $V=3.14\times12\times12$.
$12\times12 = 144$, and $V=3.14\times144 = 452.16$ $m^{3}$.

Answer:

$452.16$ $m^{3}$