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Contents
Volumes of Revolution
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Volumes of Revolution  A
solid of revolution is formed when a region bounded by part of a curve is
rotated about a straight line.
Rotation
about x-axis:
Rotation
about y-axis:
 The
diagram shows the graph of y = 5 - 2 cos 2x.
(i)
Show that (5 - 2 cos 2x)2 = 2 cos 4x - 20 cos 2x + 27
(ii)
Hence, calculate the volume of the solid formed when the shaded region is
rotated through 2p
radians about the x-axis.
Solution:
(i) (5 - 2 cos
2x)2 = 25 - 20 cos 2x + 4 cos22x
= 25 - 20 cos 2x + 2 (cos 4x + 1)
= 2 cos 4x - 20 cos 2x + 27
(ii)
Volume of revolution
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