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

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04 Dec 2007, 09:45

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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!!

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.

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.
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

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