SOLUTION: If the height of a right circular cylinder is quadrupled and the radius is divided by three, how is the volume changed?

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Question 200090: If the height of a right circular cylinder is quadrupled and the radius is divided by three, how is the volume changed?
Answer by orca(409) About Me  (Show Source):
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Suppose the height and the radius of the original cylinder are h and r respectively. Then the volume of the original cylinder is
v+=+pi%2Ar%5E2%2Ah
The height and the radius of the newly formed cylinder are 3h and r/3 respectively. Then the volume of the newly formed cylinder is
V+=+pi%2A%28r%2F3%29%5E2%2A3h
=pi%2A%28r%5E2%2F9%29%2A3h
=%281%2F3%29%2Api%2Ar%5E2%2Ah
=%281%2F3%29%2Av
So the volume of the newly formed cylinder is only one third of the volume of the original cylinder.