Question

A cone with a slant height of 8 and a radius of 3. What is the volume?

Answer 1

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:

`\text{ Volume = }(1)/(3)\pi r^2\sqrt[]{l^2-r^2}`

Where,

r = radius

l = slant height

We get,

`\text{ Volume = }(1)/(3)\pi r^2\sqrt[]{l^2-r^2}`
`\text{ = }(1)/(3)\pi(3)^2\sqrt[]{(8)^2-(3)^2_{}}`
`\text{ = }(9)/(3)\pi^{}\sqrt[]{64-9^{}_{}}`
`\text{ = }3\pi^{}\sqrt[]{55^{}_{}}`
`\text{ = 3}\sqrt[]{55}\pi\text{ or 69.89602405387 }\approx\text{ 69.90}`

Therefore, the volume of the cone is 3√55π or 69.90.