SOLUTION: a standard 8/1/2x11. sheet of paper is rolled along its short side to form a cylinder as shown. a second sheet of the same measurements as the first one is rolled along its longer

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Question 523491: a standard 8/1/2x11. sheet of paper is rolled along its short side to form a cylinder as shown. a second sheet of the same measurements as the first one is rolled along its longer side to forma second cylinde.
.there is no overlap
.will the taller cylinder have the same volume, greater volume, or less volume than that of the short cylinder?
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
One cylinder will have dimensions as follows:
circumference = 8.5 = pi*d = pi*2*r
r = (8.5)/ (2*pi)
height = 11
area of base of cylinder = pi*r^2 = pi * ( 8.5/(2*pi) )^2
volume = 11 *pi * ( 8.5/(2*pi) )^2 = 198.6875/pi
.
The other cylinder:
circumference = 11
r = 11/ (2*pi)
height = 8.5
area of base = pi * ( 11/(2*pi) )^2
volume = 8.5* pi * ( 11/(2*pi) )^2 = 257.125/pi
.