Question

I have a solid gold cone with a height of eight inches. The cone has twice the volume of a sphere with a radius of 7 inches. What is the radius of my cone?

Answer 1

Explanation:

Let's start out with the formulas for the volumes of the cone and the sphere.

`V_(c)=(1)/(3)\pi r^2h` and
`V_(s)=(4)/(3)\pi r^3`

We are given that height of the cone is 8 and the radius of the sphere is 7. We are also told then that the volume of the cone is 2 times the volume of the sphere, which algebraically, looks like this:

`V_c=2V_s` so let's set up our equation like that then, shall we?

`(1)/(3)\pi r^2(8)=2[(4)/(3)\pi (7)^3]` Let's simplify that a bit:

`(8)/(3)\pi r^2=(8)/(3)\pi (343)`

The reason for that is because it's apparent now that the 8/3 cancel each other out, as does the π, leaving us simply with:

`r^2=343`

Take the square root of both sides to get that

r = 18.52 in.

Not sure how much you need to round.