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# A sheet of paper 8 units long and 6 units wide is rolled

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Senior Manager
Joined: 30 Aug 2003
Posts: 322
Location: dallas , tx
A sheet of paper 8 units long and 6 units wide is rolled [#permalink]

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30 Dec 2003, 09:57
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A sheet of paper 8 units long and 6 units wide is rolled into a cylinder 8 units in height. What is the volume of the cylinder?

48/pi
72/pi
24/pi
9/pi
96/pi
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shubhangi

Intern
Joined: 17 Aug 2003
Posts: 38
Location: USA

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30 Dec 2003, 11:05
With assumptions

circumfrence = 2*pi*r = 6

therefore r = 3/pi

volume = 8*pi*r^2 = 8 *pi*(9/pi^2) = 72/pi

B?
Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

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30 Dec 2003, 11:13
Okay, Shubanghi - now you tell us what the Surface Area of the cylinder is with explanation! (let Shubanghi answer this please!)
Senior Manager
Joined: 30 Aug 2003
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Location: dallas , tx

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30 Dec 2003, 11:26
Well , i am not good in Geometry at all..but still i will give a try.

its asks the volume..so we must find out the radius of the cyclinder.Since the width is 6 ..the circumfernece should be 6 too..then find the radius.
6=2*pi*r..tf..(6/2*pi)=(2*pi*r/2*pi) = 3/pi=r......(1)
volume = pi*r^2 *h
so pi*3/pi*3/pi*8=72/pi
...
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shubhangi

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30 Dec 2003, 11:35
okay now surface area of cyclinder is =2*pi r*h +2*pi*r^2
so 2*pi*3/pi*8 + 2*pi*3*pi*3/pi = 66/pi..right??
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shubhangi

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30 Dec 2003, 11:37
Good try. Let me leave you with the formula: SA Cylinder = 2 Circles + Rectangle: Thus, 2(Pi*r^2) + 2 pi*r*h

Give it a shot!

Last edited by Titleist on 30 Dec 2003, 12:16, edited 1 time in total.
Director
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30 Dec 2003, 11:50
Shubanghi,

This is how I did it:

SA cylinder = 2prh+2(pi*r^2)

we established that r=3/pi

plug in

2*pi*3/pi*8 + 2(pi*3/pi^2)

48 + 2(9/pi) = 48 + 18/pi = 48pi +18
Director
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30 Dec 2003, 12:07
Okay Shubanghi,

A tougher question for you: this would be considered a difficult question.

If the surface area of a cylinder is 400pi feet and the height of the cylinder is 17 feet, then what is the diameter of this cylinder's circular base?

a)14
b)15.24
c)15.9
d)16
e)16.33

Once you solved this problem, you'll have mastered GMAT cylinder problems!
Director
Joined: 14 Oct 2003
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Location: On Vacation at My Crawford, Texas Ranch

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30 Dec 2003, 12:50
No, try backsolving if you can.
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4288

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30 Dec 2003, 13:04
Wow, that pix is way too big Titleist. I understand your promotion to VP but still...
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Best Regards,

Paul

Director
Joined: 28 Oct 2003
Posts: 501
Location: 55405

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30 Dec 2003, 13:08
Ditto on the Titleist avatar.

I could wretch!
Senior Manager
Joined: 30 Aug 2003
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30 Dec 2003, 13:09
making me nervous.. .what is the right answer
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shubhangi

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30 Dec 2003, 13:09
"I didn't tell her to lie under deposition - I told her to lie there in that position!!!!"

-Bubba

Last edited by Titleist on 30 Dec 2003, 13:46, edited 1 time in total.
Director
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30 Dec 2003, 13:32
400pi=2pi*r^2+2pi*r*h

given: h=17

thus,

400pi=2pi*r^2+2pi*r17

400pi=2pi(r^2+17r)

200=r^2+17r

0=r^2+17r-200

0=(r+25)(r-8)

thus r=(-25,8)

thus we pick r=8

we're not done yet

d=2r

Last edited by Titleist on 30 Dec 2003, 13:47, edited 1 time in total.
GMAT Club Legend
Joined: 15 Dec 2003
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30 Dec 2003, 13:47
That line is from Conan O'Brian Indeed, I got D 16 as well
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Best Regards,

Paul

Director
Joined: 14 Oct 2003
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Location: On Vacation at My Crawford, Texas Ranch

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30 Dec 2003, 13:49
Yes! You're on fire Paul!
Director
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30 Dec 2003, 14:43
One more question and we'll call it a night as far as cylinders are concerned.

A cylindrical storage tank containing the liquid chemical, ammonium xylenesulfonate, is being filled at a rate of pi cubic meters per second. Structural engineers are also working on the tank and they are surveying the dimensions of the tank. The tank stands 10 meters tall. If the tank was empty before being filled and if took 13.5 minutes to fill then what is the diameter of the tank?

a) 8 meters
b) 9 meters
c)12 meters
d)16 meters
e)18 meters
Director
Joined: 13 Nov 2003
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30 Dec 2003, 14:49
Titleist wrote:
One more question and we'll call it a night as far as cylinders are concerned.

A cylindrical storage tank containing the liquid chemical, ammonium xylenesulfonate, is being filled at a rate of pi cubic meters per second. Structural engineers are also working on the tank and they are surveying the dimensions of the tank. The tank stands 10 meters tall. If the tank was empty before being filled and if took 13.5 minutes to fill then what is the diameter of the tank?

a) 8 meters
b) 9 meters
c)12 meters
d)16 meters
e)18 meters

hey, did you write this ques. if yes, where did you get "ammonium xylenesulfonate" ..?? interresting.

anyway, I got 18.
Director
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30 Dec 2003, 14:52
18 it is. Check the ingredients on your shampoo bottle.
Director
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30 Dec 2003, 14:56
Titleist wrote:
18 it is. Check the ingredients on your shampoo bottle.

hmmm..that's something to ponder

solution:
vol/time = pi*R^2*H / time = pi
H=10
solve for 2R---> Dia
30 Dec 2003, 14:56

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