The radius of a right circular cylinder is decreased by 20% and its height is increased by 25%. What is the absolute value of the percent change in the volume of the cylinder?

Guest Jan 1, 2019

#2**+1 **

Let the original radius = r and the original height = h

So....the original volume is pi * r^2 * h = 1 * pi * r^2 * h

So....decreasing the radius by 20% produces .80r

And increasing the height by 25% produces 1.25h

So....the new volume is pi * (.8r)^2 * 1.25h = (64/100) * (125/100) pi * r^2 *h =

(64/100) * (5/4) pi * r^2 * h = [16 * 5] / 100 * pi * r^2 * h = (80/100) * pi * r^2 * h = .8 pi * r^2 * h

"Cancelling" out the pi * r^2 * h...... the percent change in the volume is

( [ 1 - .8 ] / 1 x 100 ) % = ( .2 x 100) % = 20%

CPhill Jan 1, 2019