SOLUTION: If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then what is the volume of the change....?

Algebra ->  Volume -> SOLUTION: If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then what is the volume of the change....?      Log On


   

Question 1000283: If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then what is the volume of the change....?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
volume = pi * r^2 * h

your new r = 1/2 * the original r = (1/2 * r).
your new h = 2 * the original h = (2 * h)

formula becomes:

volume = pi * (1/2 * r)^2 * (2 * h) which becomes:

volume = pi * (1/2)^2 * r^2 * 2 * h which becomes:

volume = pi * 1/4 * r^2 * 2 * h which becomes:

volume = pi * 1/4 * 2 * r^2 * h which becomes:

volume = pi * 2/4 * r^2 * h which becomes:

volume = pi * 1/2 * r^2 * h.

the new volume is half the original volume.

here's an example:

assume the radius is equal to 4 and the height is equal to 4.

original volume is pi * 4^2 * 4 = pi * 16 * 4 = pi * 64

revised volume is pi * 2^2 * 8 = pi * 4 * 8 = pi * 32

pi * 32 is 1/2 the volume of pi * 64.