am i going crazy??

[hongwang9703]

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.

this is copied in verbatim from a mgmat practice test, arent the answers A-C, and B-D IDENTICAL!!? How could this be???
Also here is the explanation to the problem:
One of the cylinders has a height of 6 and a base circumference of 10; the other has a height of 10 and a base circumference of 6.

The cylinder with a height of 6 and a base circumference of 10 has a radius of (5/ ). Its volume is equal to r2h, or (5/ )2(6) or 150/ .

The cylinder with a height of 10 and a base circumference of 6, however, has a radius of (3/ ). Its volume is equal to r2h, or (3/ )2(10) or 90/ .

We can see that the volume of the cylinder with a height of 6 is 60/ inches greater than that of the cylinder with a height of 10. It makes sense in this case that the cylinder with the greater radius will have the greater volume since the radius is squared in the volume formula. The correct answer is B.

Can anyone please explain how they came up with two cylinders with different height and circumference??

[xcusemeplz2009]

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.

this is copied in verbatim from a mgmat practice test, arent the answers A-C, and B-D IDENTICAL!!? How could this be???
Also here is the explanation to the problem:
One of the cylinders has a height of 6 and a base circumference of 10; the other has a height of 10 and a base circumference of 6.

The cylinder with a height of 6 and a base circumference of 10 has a radius of (5/ ). Its volume is equal to r2h, or (5/ )2(6) or 150/ .

The cylinder with a height of 10 and a base circumference of 6, however, has a radius of (3/ ). Its volume is equal to r2h, or (3/ )2(10) or 90/ .

We can see that the volume of the cylinder with a height of 6 is 60/ inches greater than that of the cylinder with a height of 10. It makes sense in this case that the cylinder with the greater radius will have the greater volume since the radius is squared in the volume formula. The correct answer is B.

Can anyone please explain how they came up with two cylinders with different height and circumference??

as per the information there are two ways to make cylinder ; one with 10 as a base and one with 6 as a base.

case1) when base is 10;that means circumference of the bas of the cylinder is 10;therefor r=5/pi
and v=150/pi

case 2) when base is 6, r=3/pi;v=90/pi

diff v1-v2=60/pi

only B is close to this....

A and C ; B and D are different
A;-60/
C:-60 same for B and D