Problem Solving

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/p cubic inches greater than the volume of the cylinder with
height 6.
B The volume of the cylinder with height 6 is 60/p cubic inches greater than the volume of the cylinder with
height 10.
C The volume of the cylinder with height 10 is 60p cubic inches greater than the volume of the cylinder with
height 6.
D The volume of the cylinder with height 6 is 60p cubic inches greater than the volume of the cylinder with
height 10.
E The volume of the cylinder with height 6 is 240/p cubic inches greater than the volume of the cylinder with
height 10.

OE B

Can Anyone explain me the reasoning?
I have doubts in it.

akash singhal 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/p cubic inches greater than the volume of the cylinder with
height 6.
B The volume of the cylinder with height 6 is 60/p cubic inches greater than the volume of the cylinder with
height 10.
C The volume of the cylinder with height 10 is 60p cubic inches greater than the volume of the cylinder with
height 6.
D The volume of the cylinder with height 6 is 60p cubic inches greater than the volume of the cylinder with
height 10.
E The volume of the cylinder with height 6 is 240/p cubic inches greater than the volume of the cylinder with
height 10.

OE B

Can Anyone explain me the reasoning?
I have doubts in it.

Dimension of paper = 10 x 6

To form a cylinder from this we have 2 ways:
1) height = 6 and circumference = 10; 2*pi*r1 =10, r1 = 5/pi
2) height = 10 and circumference = 6; 2*pi*r2 = 6, r2 = 3/pi

Volume of cylinder = pi * r^2 * h

1) volume when height is 6 = pi * (5/pie)^2 * 6 = 150/pi
2) volume when height is 10 = pi * (3/pie)^2 *10 = 90/pi

Thefore the volume when height is 6 is (150-90)/pi = 60/pi greater than the volume when height is 10

ans = b

Hi Brent,

I am little confused about this question because my answers yield to the 60pi not 60/pi; ei: D

here is how i did it; please tell me what i did wrong.

case1, H=6 , R=5

since volume of a cylinder is pi x r^2 x H

volume = 150pi

case2: H=10, R=3

volume= 90pi

Hence case 1 is greater than case 2 by 60pi

please explain to me what i did wrong here.

Brent@GMATPrepNow wrote: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

Amrabdelnaby wrote: case1, H=6 , R=5

since volume of a cylinder is pi x r^2 x H

volume = 150pi

case2: H=10, R=3

volume= 90pi

The issue is that your sheet of paper's dimensions become the height and the circumference of the cylinder's base, not the radius of the cylinder's base. (Roll a piece of paper into a cylinder and you can see why this is.) You're using 5 and 3 as possible radii when 10 and 6 should represent possible circumferences, yielding radii of 5/Ï€ and 3/Ï€, respectively. Everything else is right though, so your geometry is on the right track!