Given:
a.) A cone with a slant height of 8 and a radius of 3.
To be able to get the volume of the cone with only the slant height and radius given, we use the following formula:
[tex]\text{ Volume = }\frac{1}{3}\pi r^2\sqrt[]{l^2-r^2}[/tex]Where,
r = radius
l = slant height
We get,
[tex]\text{ Volume = }\frac{1}{3}\pi r^2\sqrt[]{l^2-r^2}[/tex][tex]\text{ = }\frac{1}{3}\pi(3)^2\sqrt[]{(8)^2-(3)^2_{}}[/tex][tex]\text{ = }\frac{9}{3}\pi^{}\sqrt[]{64-9^{}_{}}[/tex][tex]\text{ = }3\pi^{}\sqrt[]{55^{}_{}}[/tex][tex]\text{ = 3}\sqrt[]{55}\pi\text{ or 69.89602405387 }\approx\text{ 69.90}[/tex]Therefore, the volume of the cone is 3√55π or 69.90.
