A GRE Question- Cylinder and Volume

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Homework Help Overview

The problem involves comparing the volumes of two cylinders formed by rolling a 9x12 inch sheet of paper. Jack rolls the paper using the 9-inch edges, while Jill uses the 12-inch edges. The discussion centers around understanding how the circumferences of the cylinders are determined and their implications for calculating volume.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the dimensions of the paper and the resulting cylinder's dimensions, particularly focusing on how the circumferences are derived based on the edges used for rolling. There is an attempt to clarify the roles of height and circumference in the context of the problem.

Discussion Status

Some participants are seeking clarification on the derivation of the circumferences for each cylinder, indicating a productive exploration of the problem's setup. One participant expresses understanding after further reflection.

Contextual Notes

The discussion highlights potential confusion regarding the definitions of height and circumference in relation to the dimensions of the paper. There is no explicit consensus on the interpretation of the problem, but participants are engaging with the concepts involved.

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Homework Statement


Jack and Jill each roll a sheet of 9X12 paper to form a cylinder.
Jack tapes the two 9-inch edges together.
Jill tapes the two 12-inch edges together.

Which is greater?
The volume of Jack's Cylinder
or
The volume of Jill's cylinder.

Homework Equations



Cylinder Volume: V=pi*r^2*h

The Attempt at a Solution



The problem that I was facing with this question was finding the radii.
However, I looked at the solutions and it says that
Jack's cylinder has a circumference of 12
and Jill's cylinder has a circumference of 9

Jack's height is 9
Jill's height is 12

I don't understand how they derived the circumferences ?!
once I know the circumference I can find the radius.

Thanks.
 
Last edited:
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There's two ways to roll a 9x12 inch piece of paper. If you use the 12 inch side to make the circumference then the 9 inch side must be the height, right? And vice versa? Maybe I don't understand what your question is.
 
Last edited:
Dick said:
There's two ways to roll a 9x12 inch piece of paper. If you use the 12 inch side to make the circumference then the 9 inch side must be the height, right? And vice versa? Maybe I don't understand what your question is.

I'm sorry, my question wasn't clear.
How did they conclude that the circumference is 12 for Jack
and 9 for Jill
 
ohhh, I see it now :\

Thanks.
 

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