Question

1. what is the volume of a cone with a slant height of 15 m and a radius of 12 m?

Explanation:

Step1: Find the height of the cone.

Use the Pythagorean theorem $h = \sqrt{l^{2}-r^{2}}$, where $l = 15$ m is the slant - height and $r = 12$ m is the radius.
$h=\sqrt{15^{2}-12^{2}}=\sqrt{(15 + 12)(15 - 12)}=\sqrt{27\times3}=\sqrt{81}=9$ m

Step2: Calculate the volume of the cone.

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 12$ m and $h = 9$ m into the formula.
$V=\frac{1}{3}\pi\times12^{2}\times9=\frac{1}{3}\pi\times144\times9 = 432\pi$ $m^{3}$

Answer:

$432\pi$ $m^{3}$