# Kapaln math #22

Discussion in 'DAT Discussions' started by Greensalad, Apr 18, 2007.

1. ### Greensalad 10+ Year Member

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22. If a diameter of a cylinder is increased by 20% and the height is decreased by 16 2/3 %, by what percent is the volume changed?
A. -10
B. 10
C. 20
D. 24
E. 83 1/2

I can do this problem but I would need more than a minute. What's the quickest way to do it?

2. OP

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Alright I can do it in 40 seconds if I plug in numbers, but I knew which numbers to plug in before I started doing the problem. I don't think plugging in numbers is a good idea.

3. ### infernobutterfl Pyro user 7+ Year Member

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We are supposed to do the math out by hand? (possible, but that is just a waste of time and effort.) if only the 24% was not there, then the answer would have been much easier. (one could guess-timate the answer)

4. ### Streetwolf Ultra Senior Member Dentist 7+ Year Member

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Volume = pi*r^2*h
New Volume = pi*(1.2r)^2*(0.833h)

We write 1.2 as (6/5) and 0.833 as (5/6).

So we have New Volume = pi*(6/5)^2*r^2*(5/6)*h
New Volume = (6/5)pi*r^2*h

The new volume is 1.2 * the old volume, so the new volume is increased by 20%.

C.

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5. OP

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Thanks. Your QR's probably a 30.

6. ### Streetwolf Ultra Senior Member Dentist 7+ Year Member

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28. Dunno if that was perfect or not

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