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Question 1016906: A rectangle with length and width equal to 6 cm and 4 cm respectively is revolved about its length.
A. What is the volume of the right circular cylinder formed?
B. Suppose the rectangle is revolved about its width instead, what is the volume of the cylinder formed?
C. Compare the volumes of the two cylinders.
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
A rectangle with length and width equal to 6 cm and 4 cm respectively is revolved about its length.
A. What is the volume of the right circular cylinder formed?
B. Suppose the rectangle is revolved about its width instead, what is the volume of the cylinder formed?
C. Compare the volumes of the two cylinders.
Answers:
A) If the rectangle is revolved about its length
then the width becomes the cylinder's radius.
Therefore the cylinder has a radius of 4 cm and
a height of 6 cm.
Volume of a cylinder = Pi x r^2 x h (r = radius, h = height)
Volume = Pi x 4^2 x 6
Volume = 301.6 cm^3 (1 decimal place)
B) if the rectangle is rotated around its width
then the length becomes the cylinder's radius.
Therefore the cylinder has a radius of 6 cm and a height
of 4 cm
Volume of a cylinder = Pi x r^2 x h (r = radius, h = height)
Volume = Pi x 6^2 x 4
Volume = 452.4 cm^3 (1 decimal place)
C) Rotation round the length gives a cylinder
of 301.6 cm^3
Rotation round the width gives a cylinder of
452.4 cm^3
Hope this helps :-)
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