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Question 287598: A right circular cylinder is given. If the radius is increased by 25% then the volume will stay the same if the height is increased/decreased by what percent?
(a) Increased by 64% (b) Decreased by 36% (c) Decreased by 25%
(d) Increased by 25% (e) None of the above
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! A right circular cylinder is given. If the radius is increased by 25% then the volume will stay the same if the height is increased/decreased by what percent?
(a) Increased by 64% (b) Decreased by 36% (c) Decreased by 25%
(d) Increased by 25% (e) None of the above
Let r be the original radius, h the original height and H the new increased height. Then we have:
1.) volume of original cylinder = pi*(r^2)*h
2.) volume of cylinder with increased radius = pi*(1.25r)^2*H
For the volume not to change we must have:
pi*(r^2)*h = pi*(5/4*r)^2*H
pi*(r^2)*h = pi*25/16*r^2*H
Divide both sides above by pi:
r^2*h = (25/16)*r^2*H
Divide both sides by r^2:
h = (25/16)*H
H = (16/25)*h
H = .64*h
The height must be DECREASED by .36, that is 36%.
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