SOLUTION: A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the

Algebra ->  Volume -> SOLUTION: A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the      Log On


   

Question 933612: A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For the cone,
V%5Bk1%5D=%28pi%2F3%29R%5E2%2AH

n%5Bk%5D=%28%283pi%29%2F2%29%2F%28pi%2F3%29
n%5Bk%5D=9%2F2
.
.
.
For the cylinder,
V%5Bc1%5D=pi%2AR%5E2%2AH
V%5Bc2%5D=pi%2AR%5E2%2A%282H%29
n%5Bc%5D=V%5Bc2%5D%2FV%5Bc1%5D=2
Cone has greatest change in volume.