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