SOLUTION: Hello, I have two questions I don't quite understand: 1. A sphere and a cube have the same volume. Find the ratio of the length of the side of the cube to the radius of the

Algebra ->  Finance -> SOLUTION: Hello, I have two questions I don't quite understand: 1. A sphere and a cube have the same volume. Find the ratio of the length of the side of the cube to the radius of the       Log On


   

Question 1081563: Hello,
I have two questions I don't quite understand:
1. A sphere and a cube have the same volume. Find the ratio of the length of the side of the cube to the radius of the sphere.
2. A sphere has radius r. A cone has the same base radius as the sphere and height h. If they have the same volume, find the ratio of h : r.
Thank you!
Josh
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a sphere,
V%5Bs%5D=%284%2F3%29pi%2AR%5E3
For a cube,
V%5Bc%5D=s%5E3
So,
%284%2F3%29pi%2AR%5E3=s%5E3
s%5E3%2FR%5E3=%284%2F3%29pi
s%2FR=root%283%2C%284%2F3%29pi%29
.
.
.
For a cone,
V%5Bcone%5D=%28pi%2F3%29r%5E2%2Ah
So,
%28pi%2F3%29r%5E2%2Ah=%284%2F3%29pi%2Ar%5E3
h=4r
h%2Fr=4