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?

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

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

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

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

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

OAB

Rich's answer is pretty hard to read with the carets, so here's how that would look with proper notation.

If the cylinder has a height of 6 and a circumference of 10, we'd have

h = 6
c = 10
r = 10/(2π) = 5/π 
volume = 6 * (5/π)² = 150/π²

If the cylinder has a height of 10 and a circumference of 6, we'd have

h = 10
c = 6
r = 6/2π = 3/π 
volume = 10 * (3/π)² = 90/π²

Since 150/π² > 90/π², the cylinder with the height of 6 has a greater volume.