Question

find the volume of a cone with a base diameter of 6 m and a height of 8 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

The radius $r$ is half of the diameter. Given diameter $d = 6$ m, so $r=\frac{d}{2}=\frac{6}{2}=3$ m.

Step2: Use the cone - volume formula

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 3$ m, $h = 8$ m and $\pi=3.14$ into the formula.
$V=\frac{1}{3}\times3.14\times3^{2}\times8$.
First, calculate $3^{2}=9$. Then $V=\frac{1}{3}\times3.14\times9\times8$.
$\frac{1}{3}\times9 = 3$, so $V=3.14\times3\times8$.
$3.14\times3 = 9.42$, and $9.42\times8=75.36$ $m^{3}$.

Answer:

$75.36$ $m^{3}$