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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?

 Jan 1, 2019
 #1
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*** deleted ***    misread Q

 Jan 1, 2019
edited by Guest  Jan 1, 2019
 #2
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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%

 

 

cool cool cool

 Jan 1, 2019
edited by CPhill  Jan 1, 2019

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