SOLUTION: Hi, I really need help with this question: A cone has the same base radius as the radius of a sphere. If the volumes of the cone and the sphere are equal, by what factor is

Question 1081843: Hi, I really need help with this question:

A cone has the same base radius as the radius of a sphere. If the volumes of the cone and the sphere are equal, by what factor is the height of the cone larger than its base radius?
Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The volume of the sphere is
Vs = (4/3)*pi*r^3
where r is the radius

The volume of the cone is
Vc = (1/3)*pi*r^2*h
where r is the radius of the base and h is the height

Note: Since the problem states that "A cone has the same base radius as the radius of a sphere", we can use the variable r twice.

Since we're told that "the volumes of the cone and the sphere are equal", we can say
Vc = Vs
(1/3)*pi*r^2*h = (4/3)*pi*r^3
3*(1/3)*pi*r^2*h = 3*(4/3)*pi*r^3 multiply both sides by 3
pi*r^2*h = 4*pi*r^3
(pi*r^2*h)/pi = (4*pi*r^3)/pi divide both sides by pi
r^2*h = 4*r^3
(r^2*h)/(r^2) = (4*r^3)/(r^2) divide both sides by r^2
h = 4*r

After isolating h, we get h = 4*r indicating that the height is 4 times the base radius.
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