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# A 10-by-6 inch piece of paper is used to form the lateral

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A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  04 Dec 2007, 08:45
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the cylinder, which of the following must be true of the two possible cylinders that can be formed?

A, The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B, The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C, The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D, The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E, The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

The answer is B. First and foremost, how do they get two cylinders. I don't see anywhere mentioning of two cylinders. I assumed given a paper size, I suppose create one cylinder. Please explain. Thanks in advance!!

Regards
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Well, the problem did not say to create two cylinders. You still create one cylinder per paper.

But with the dimension of the paper 10x6, you are able to create two different type of cylinder. Either the one with height 6 and circumference of the circle base to be 10, or the one with height 10 and the circumference of the circle base to be 6. And when you calculate the volume of these two different type of cylinder, you get B as your answer.
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Thanks eileen1017 as always!! You've been a great help.
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Re: Cylindar [#permalink]  10 Jan 2008, 11:41
I still dont understand this question.

A cylinder is pi*R^2*Height
What is the "lateral surface" of a cylinder?
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Re: Cylindar [#permalink]  10 Jan 2008, 11:53
B.
150 pi for the cylinder with hieght of 6 minus 90 pi for the one with height of 10

http://www.mathguide.com/lessons/Surfac ... #cylinders
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Re: Cylindar [#permalink]  10 Jan 2008, 12:00
allright i got it. the lateral side is the wraparound of the cylinder. we can create 2 different cylinders by turning the paper on its vertical and horizontal sides.
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Re: Cylindar [#permalink]  11 Jan 2008, 03:12
CaspAreaGuy wrote:
B.
150 pi for the cylinder with hieght of 6 minus 90 pi for the one with height of 10

http://www.mathguide.com/lessons/Surfac ... #cylinders

I get 150 pi and 90 pi - but doesn't this make the answer D, 60pi (not B 60/pi)??
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Re: Cylindar [#permalink]  11 Jan 2008, 05:04
if h = 10
then c = 6

c= pi * D
6 = pi 2 R
3 = pi R
R = 3/pi

V=piR^2 * H
V = pi (3/pi)^2 * 10
V = 9/pi * 10
V = 90/pi

NOT 90pi
same with the other scenario
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Re: Cylindar [#permalink]  11 Jan 2008, 06:15
Thanks - I stupidly looked at this and said R=3 / R=5!
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Re: Cylindar [#permalink]  11 Jan 2008, 06:50
pinal2 wrote:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the cylinder, which of the following must be true of the two possible cylinders that can be formed?

A, The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B, The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C, The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D, The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E, The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

The answer is B. First and foremost, how do they get two cylinders. I don't see anywhere mentioning of two cylinders. I assumed given a paper size, I suppose create one cylinder. Please explain. Thanks in advance!!

Regards

volume of cylinder is pi*R^2*h
if height is 10 then circumference is 6 => 2*pi*R=6 => R=3/pi => volume pi*9/pi^2*10=90/pi
if height is 6 then circumference is 10 => 2*pi*R=10 => R=5/pi => volume pi*25/pi^2*6=150/pi

150/pi-90/pi=60/pi
Re: Cylindar   [#permalink] 11 Jan 2008, 06:50
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