Question 90978This question is from textbook
: A standard 8 1/2" x 11" sheet of paper is rolled along it's short side to form a cylinder. A second sheet of standard 8 1/2" x 11" sheet of paper is rolled along it's longer side to form a second cylinder. There is no overlap. Will the taller cylinder have the same volume, greater volume, or less volume than that of the short cylinder?
This question is from textbook
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A standard 8 1/2" x 11" sheet of paper is rolled along it's short side to form a cylinder. A second sheet of standard 8 1/2" x 11" sheet of paper is rolled along it's longer side to form a second cylinder. There is no overlap. Will the taller cylinder have the same volume, greater volume, or less volume than that of the short cylinder?
:
V = pi*r^2*h
:
Thinking about it, you would say that the cylinder with the greater diameter,
(because of r^2) would have the greater volume, therefore the shorter cylinder
would have the greater volume.
:
To confirm this
:
The shorter cylinder:
Find the radius
2r*pi = 11
r = 11/2pi
r = 1.75 inches
V = pi*1.75^2*8.5
V = 81.78 cu inches
:
The taller cylinder:
Find the radius
2r*pi = 8.5
r = 8.5/2pi
r = 1.35 inches
V = pi*1.35^2*11
V = 62.98 cu inches
;
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