Answer:
Step-by-step explanation:
Let's start out with the formulas for the volumes of the cone and the sphere.
[tex]V_{c}=\frac{1}{3}\pi r^2h[/tex] and [tex]V_{s}=\frac{4}{3}\pi r^3[/tex]
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:
[tex]V_c=2V_s[/tex] so let's set up our equation like that then, shall we?
[tex]\frac{1}{3}\pi r^2(8)=2[\frac{4}{3}\pi (7)^3][/tex] Let's simplify that a bit:
[tex]\frac{8}{3}\pi r^2=\frac{8}{3}\pi (343)[/tex]
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:
[tex]r^2=343[/tex]
Take the square root of both sides to get that
r = 18.52 in.
Not sure how much you need to round.
