Manhattan Cat Question in regards to cylinders

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bpolley00: Master | Next Rank: 500 Posts; Posts: 192; Joined: Wed Jul 11, 2012 5:04 pmFollowed by: 5 members; Thanked: 20 times; GMAT Score:650

by bpolley00 » Mon Feb 18, 2013 1:55 pm

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 60 Pie 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.

Can someone explain why this isn't D?

Here is how I did it
V1=Pie*(R^2)*H
V2= Pie*(R^2)*H

For V1 R=3 H=10 V1= 90Pie
for V2 R=5 H= 6 V2= 150pie
Thus H=6 is 60pie greater than H=10? Why is it 60/Pie instead of 60pie

Source: Beat The GMAT — Quantitative Reasoning | Mon Feb 18, 2013 1:55 pm

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Tue Feb 19, 2013 9:24 am

Be careful about your assumptions! When we bend the paper to form a cylinder, the edge of that paper becomes the circumference of the circle. I think your mistake was probably adding an imaginary pi to that circumference.

You're right that V = pi(r^2)h. But think about how you calculate that radius...

For the cylinder with the height of 6, the side that's 10 forms the circumference. Circumference = pi*diameter, or C = 2(pi)(r).
10 = 2(pi)(r), then the radius does not equal 5. We still have to divide by pi. It equals 5/pi.
So, V = pi((5/pi)^2)h
V = pi(25/pi^2)6
V = (25/pi)6 = 150/pi

For the cylinder with a height of 10, the circumference is 6.
6 = 2(pi)(r)
r = 3/pi
V = pi((3/pi)^2)h
V = (9/pi)10 = 90/pi

Thus, the answer is B, not D.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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