Help W/ a problem

[mets9131]

For Pre calc cannot figure this out even though I know it is simple.

A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high

A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high

There is no overlap

A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain
C. If a shett 11 X 17 inches paper was used to make a cylinder 17 inches tall, how would its volume and surface area compare to the volume and surface area of the 8 1/2 inch tall cylinder? Explain

[OfficeShredder]

Do all these cylinders have the same radius? Because you can roll paper looser or tighter, and that dramatically affects the question.

[HallsofIvy]

OfficeShredder, the original post said "with no overlap".

Isn't it obvious that the surface area of the two cylinders is exactly the area of the sheet of paper they are made from and, so, the same?

I assume that you are making a cylinder with CIRCUMFERENCE the same as the long side of the paper, 11 inches. You know, I hope, that the circumference of a circle is 2pi r so from 2pi r= 11, you can find r= 11/2pi. Then the volume of the cylinder is pi r^2 h= pi(121/4pi^2)(8.5)= 1028.5/(4pi).The radius of the cylinder rolled the other way is given by 2pi r= 8.5 or r= 8.5/(2pi) so the volume of the cylinder is pi(72.25/(4pi^2)(11)= 794.75/(4pi).
The "r" is squared while "h" isn't so the larger area will be the cylinder with the larger radius: roll along its shorter side.

Notice that in the area problem, the surface area is 2pi r h. Since neither r nor h is squared, it doesn't matter which is which- both ways give the same surface area.

[HallsofIvy]

Once again, the "spam" filter wouldn't allow this. When I tried cutting some text to see where the problem was, I got back to exactly the original text and, this time, it passed it!

[Mr. Robin Parsons]

Once again, the "spam" filter wouldn't allow this. When I tried cutting some text to see where the problem was, I got back to exactly the original text and, this time, it passed it!
It was your usage of this word >> CIRC UMFERENCE << which, apparently, worked for you, but will not work for me which is why (I) spaced it out
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Doesn't work either, weird for a Physicsmathforums, really weird