Question

find the volume of a cone with a base diameter of 7 m and a height of 11 m. write the exact volume in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius

The diameter $d = 7$ m, and the radius $r=\frac{d}{2}=\frac{7}{2}$ m.

Step2: Apply the cone - volume formula

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = \frac{7}{2}$ m and $h = 11$ m into the formula.
$V=\frac{1}{3}\pi\times(\frac{7}{2})^{2}\times11$.
First, calculate $(\frac{7}{2})^{2}=\frac{49}{4}$. Then $V=\frac{1}{3}\pi\times\frac{49}{4}\times11=\frac{539}{12}\pi$ $m^{3}$.

Answer:

$\frac{539}{12}\pi$ $m^{3}$