SOLUTION: the radius of a cylinder is increased by 15% and its height is decreased by 20%. Find the percentage change in the volume of the cylinder.

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Question 903866: the radius of a cylinder is increased by 15% and its height is decreased by 20%. Find the percentage change in the volume of the cylinder.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
V cylinder = pi*r^2*h
Volume
V1= pi*r1^2*h1
volume after change in radius and height
V2= pi*r2^2*h2
r2= 1+15/100 = 1+.15=1.15r1

h2= 1-20/100 = 1-0.2 = 0.8h1
V2= pi*(1.15r1)^2*(0.8h1)
=pi*1.32r1^2*0.8h1
=1.06pir1^2h1^2
Increase in volume = 1.06pir1^2h1^2-pir1^2h1^2
=0.06pir1^2h1^2
increase in volume/original volume * 100
(0.06pir1^2h1^2/pir1^2h1^2)*100
=6%