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?

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) (Show Source): You can put this solution on YOUR website!
The volume, , of a cone with radius and height is calculated as

In that expression, is the area of the base of the cone.

If the radius is quadrupled, the new radius would be .
Then, the area of the base would be , and that would be times more area for the base.

If the height is reduced to of the original height, the new height would be .

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

That is of the original cone's volume.
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