SOLUTION: How does the volume of a cone change when the radius is quadrupled and the height is reduced to 1/5 of its original size?

Algebra ->  Volume -> SOLUTION: How does the volume of a cone change when the radius is quadrupled and the height is reduced to 1/5 of its original size?       Log On


   

Question 882692: How does the volume of a cone change when the radius is quadrupled and the height is reduced to 1/5 of its original size?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The volume, V , of a cone with radius r and height h is calculated as
V=%281%2F3%29%28pi%2Ar%5E2%29%2Ah
In that expression, pi%2Ar%5E2 is the area of the base of the cone.

If the radius is quadrupled, the new radius would be 4r .
Then, the area of the base would be pi%2A%284r%5E2%29=pi%2A4%5E2%2Ar%5E3=pi%2A16%2Ar%5E2=16%2A%28pi%2Ar%5E2%29 , and that would be 16 times more area for the base.

If the height is reduced to 1%2F5 of the original height, the new height would be %281%2F5%29%2Ah .

If the radius is quadrupled, and the height is reduced to 1%2F5 of the original height, the new cone volume will be

That is 16%2F5 of the original cone's volume.