Cylinders

[Mclaughlin]

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/ cubic inches greater than the volume of the cylinder with height 6.


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


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


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


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


OA is B

[subha_sri8]

Answer is B.

The explanation is when the base is 6 inches we get the circumference of the base (2* pi* r = 6) . Therefore R= 3/pi.

Now let us calculate the Area with the base radius as 3/pi and height as 10.
So the area is (pi*r^2*h) = pi *(3/pi)^2*10 = 90/pi.

The are with the base circumference as 10 and height as 6 is = 150/pi

Therefore the difference between two areas is 150/pi - 90/pi = 60/pi.

Thus the cylinder with height 6 is 60/pi greater than the cylinder with height 10.

I hope that clarifies.

[abcdefg]

I get the answer and the algebra behind it but when i was doing this problem the word "lateral surface" confused me.

1. What does lateral surface mean? Basically the shell or the surface area?
2. If we have 1 piece of paper, how can the volume change? Arn't they just the same cylinder except flipped on its side?

[Stuart@KaplanGMAT]

I get the answer and the algebra behind it but when i was doing this problem the word "lateral surface" confused me.

1. What does lateral surface mean? Basically the shell or the surface area?
2. If we have 1 piece of paper, how can the volume change? Arn't they just the same cylinder except flipped on its side?

Lateral surface means we're only using the paper to form the rounded area of the cylinder, not the top or the bottom.

Picture wrapping a piece of paper around a can that's sitting on a table.

There are two different ways we can wrap the paper around the can- we can put either the short edge or the long edge of the paper perpedicular to the table. In the first case the circumference of the cylinder would be 6; in the second case the circumference would be 10. In the first case we create a taller, thinner cylinder; in the second a shorter, fatter one.

[rahul.s]

is this a gmat-like problem?

[RHINO]

This is a problem taken from an actual GMAT test.

This is silly I'm sure, but I thought the answer was D). Why is the pi sign in the denominator?

For example, the cylinder with a height of 10 and a base circumference of 6, has a radius of (3/pi) -- so its volume is pi(3/pi)^2 (10), which = 90/pi.

But if the formula for volume of a cylinder is Pi*r^2*h, wouldn't the volume of said cylinder be Pi*9*10=90pi, and not 90/pi?

If someone could dumb it down for me I'd appreciate it. Thanks...

[Stuart@KaplanGMAT]

This is a problem taken from an actual GMAT test.

This is silly I'm sure, but I thought the answer was D). Why is the pi sign in the denominator?

For example, the cylinder with a height of 10 and a base circumference of 6, has a radius of (3/pi) -- so its volume is pi(3/pi)^2 (10), which = 90/pi.

But if the formula for volume of a cylinder is Pi*r^2*h, wouldn't the volume of said cylinder be Pi*9*10=90pi, and not 90/pi?

If someone could dumb it down for me I'd appreciate it. Thanks...

Hi,

as you posted, the radius is 3/pi.

Volume is indeed pi(r^2)h. Plugging in:

Vol = pi ((3/pi)^2)*10
= pi(9/pi^2)*10
= (9*10) * (pi/pi^2)
= 90 * 1/pi
= 90/pi

Remember, when we square 3/pi, we get 9/pi^2.

[RHINO]

Thanks, but I still don't understand why the radius is 3/pi rather than 3pi. Given formula Pi*r^2*h, I would think we would get Pi*3^2*10 ==> Pi(9)(10) ==> 90pi. What is the step that moves Pi to the denominator? I have a feeling I'm missing something obvious but I just don't see it for some reason...

[Stuart@KaplanGMAT]

Thanks, but I still don't understand why the radius is 3/pi rather than 3pi. Given formula Pi*r^2*h, I would think we would get Pi*3^2*10 ==> Pi(9)(10) ==> 90pi. What is the step that moves Pi to the denominator? I have a feeling I'm missing something obvious but I just don't see it for some reason...

We calculate the radius based on the circumference, not the volume.

circumference = 2(pi)r

If our circumference is 6, then:

6 = 2(pi)r
6/2pi = r
3/pi = r

[prabsahi]

Hi,

I am still not clear with one aspect of this problem
To me 10 by 6 strikes as length =10 and breadth =6
Why do we have to consider 6 as the radius?

Is it because we are folding this piece of paper to be cylinder and so this entire breadth becomes
as the circumference in of the cases.

Please clarify if my reasoning is correct.

Thanks
[/quote]

[Brent@GMATPrepNow]

Hi,

I am still not clear with one aspect of this problem
To me 10 by 6 strikes as length =10 and breadth =6
Why do we have to consider 6 as the radius?

Is it because we are folding this piece of paper to be cylinder and so this entire breadth becomes
as the circumference in of the cases.

Please clarify if my reasoning is correct.

Thanks

[/quote]

A lot of people believe that the magnitude of each dimension indicates what is being measured, but this is not the case.

By the way, here are two related questions involving cylinders:
https://www.beatthegmat.com/a-cylindrica ... 71714.html
https://www.beatthegmat.com/solid-geomet ... 29356.html

Cheers,
Brent