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Question 287625: 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 Grinnell(63)   (Show Source):
You can put this solution on YOUR website! OK let us think our way thru this!
V=PI r^2 (height)
OK If we increase the radius and the volume stays the same, we have to decrease something on the other side. So something will be decreased. That leaves us B. C. and E. Now off to the races...
Pi r^2 H =Pi R^2 H
let us keep it simple! let r be 1 i.e. our initial radius.
pi (one) H= (now) pi (1.25)^2x (x is our new height, see now how it has to be less than the other height?)
Let's get rid of the pi's they cancel out--how convenient!!!!
H=1.25^2x
H=25/16 (I changed 1.25 into 5/4 and squared this)x
divide both sides by 25/16
16/25H=x
Our new height is 16/25 of the original height. Original height was decreased by 9/25. (I am just working with the fractions here!) 9/25=.36
ANSWER IS B.
Hint; Stick to the formula. Don't be afraid to let r be ONE to keep things simple! r^2 then is one.
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