A GRE Question- Cylinder and Volume

In summary, Jack and Jill each rolled a sheet of 9x12 inch paper into a cylinder, with Jack taping the 9-inch edges and Jill taping the 12-inch edges. The question asks which cylinder has a greater volume. Using the formula for cylinder volume, V=pi*r^2*h, it is necessary to know the radii of the cylinders. Since the circumference of a cylinder is equal to 2*pi*r, it can be deduced that Jack's cylinder has a circumference of 12 and Jill's has a circumference of 9. This is because if the 12-inch side is used to make the circumference, the 9-inch side must be the height, and vice versa. This information allows
  • #1
Roni1985
201
0

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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  • #2
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:
  • #3
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
 
  • #4
ohhh, I see it now :\

Thanks.
 

1. What is the formula for finding the volume of a cylinder?

The formula for finding the volume of a cylinder is V = πr2h, where V is the volume, π is the mathematical constant pi, r is the radius of the base of the cylinder, and h is the height of the cylinder.

2. Can the volume of a cylinder be negative?

No, the volume of a cylinder cannot be negative as it represents the amount of space enclosed by the cylinder and cannot have a negative value.

3. How do you convert the volume of a cylinder from cubic inches to cubic feet?

To convert the volume of a cylinder from cubic inches to cubic feet, you can divide the volume by 1728 (the number of cubic inches in a cubic foot).

4. What is the difference between the volume of a cylinder and its surface area?

The volume of a cylinder refers to the amount of space enclosed by the cylinder, while the surface area refers to the total area of the outside surfaces of the cylinder. The volume is measured in cubic units while the surface area is measured in square units.

5. Is the volume of a cylinder affected by its orientation?

No, the volume of a cylinder is not affected by its orientation as long as the dimensions (radius and height) remain the same. The formula for calculating the volume does not change with the orientation of the cylinder.

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