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 lateral surface, which of the following must be true of the two possible cylinders that can be formed?


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

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

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

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

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

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/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.

(When rommysingh posted the question, for some reason the Pi's in the answer choices did not appear. So I added them when I posted it.)

Ok. We can make two different cylinders, one with height 10 and circumference of the end circles 6, and one with height 6 and circumference of the end circles 10.

Looking at the answer choices, I see that all of them are about the difference between the volumes of the two cylinders.

On the test I would have about two minutes to get this done. I am considering whether there is any cute way to just jump to the answer, but I don't see one quickly, so I am just going to get to work calculating the volumes of the two cylinders.

The formula for the volume of a cylinder is Height x Pir².

The volume of the cylinder with height 10 is 10 x Pir². I can calculate r from the circumference of the end circles.

r = 1/2 x Circumference/Pi = 1/2 x 6/Pi = 3/Pi

So 10 x Pir² = 90/Pi

The volume of the cylinder with height 6 = 6 x Pi². r = 1/2 x 10/Pi = 5/Pi

So 6 x Pir² = 150/Pi

So the volume of the one with height 6 is 150/Pi - 90/Pi = 60/Pi greater than the volume of the one with height 10.

Choose B.

is there any typo?i thing it should be 60/pi.

sandipgumtya wrote:is there any typo?i thing it should be 60/pi.

Yes, the Pi was left out of all of the answer choices. I added it when I reposted the question.

isnt d the same answer ?