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

Algebra ->  Algebra  -> Bodies-in-space -> SOLUTION: If the height of a right circular cylinder is quadrupled and the radius is divided by three, how is the volume changed?       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

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):
You can put this solution on YOUR website!
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.