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cylinders

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by j_shreyans » Mon Oct 27, 2014 12:02 pm
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 lateral surface, 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 /pie cubic inches greater than the volume of the cylinder with height 6.

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

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

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

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

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by [email protected] » Mon Oct 27, 2014 12:38 pm
Hi j_shreyans,

This question ultimately comes down to a couple of geometry formulas:

Circumference = 2pi(radius)
Volume = (Height)pi(radius)^2

The "lateral surface of a cylinder" is a fancy way of staying "the outside of the can, but not the top nor the bottom." With a 10x6 piece of paper, we can have 2 possible cylinders:

1) Height of 10, Circumference of 6
2) Height of 6, Circumference of 10

The answers ask us to consider the volumes of the cylinders.....

1st cylinder:
Circumference = 6 = 2pi(radius)
Radius = 3/pi

Height = 10
Volume = 10pi(3/pi)^2 = 90/pi

2nd cylinder:
Circumference = 10 = 2pi(radius)
Radius = 5/pi

Height = 6
Volume = 6pi(5/pi)^2 = 150/pi

So the cylinder with a height of 6 has a volume that is 60/pi greater than the cylinder with a height of 10.

Final Answer: B

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by Matt@VeritasPrep » Fri Oct 31, 2014 9:01 am
Rich's answer is pretty hard to read with the carets, so here's how that would look with proper notation.

If the cylinder has a height of 6 and a circumference of 10, we'd have

h = 6
c = 10
r = 10/(2π) = 5/π 
volume = 6 * (5/π)² = 150/π²

If the cylinder has a height of 10 and a circumference of 6, we'd have

h = 10
c = 6
r = 6/2π = 3/π 
volume = 10 * (3/π)² = 90/π²

Since 150/π² > 90/π², the cylinder with the height of 6 has a greater volume.
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by Brent@GMATPrepNow » Fri Oct 31, 2014 11:08 am
Here's are two related questions involving cylinders:
https://www.beatthegmat.com/a-cylindrica ... 71714.html
https://www.beatthegmat.com/solid-geomet ... 29356.html

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