Analysis and Approaches for IBDP Maths Ebook 2 | Page 184

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 56
� � � � � �
1. The region bounded by the curve y � cot � x � �cosec
� x � �
� 2� � 2� and the lines �
x � ,
23
5�
x � , y � 0 is rotated through 2π radians about the x -axis. Find the exact volume of
6
the solid generated.
[6]
2. The region bounded by the curve y�ln � x� ln �
� and the lines y � 2�
, the x -axis and
the y -axis is rotated through 2π radians about the y -axis. Find the exact volume of the
solid generated.
2 2
x y
3. The region R is bounded by the curve � � 1 and the x -axis. A rugby model is
2 2
9a
4a
formed by rotating the region R through 2� about the x -axis. Show that the volume of
the rugby model formed is
3
16� a .
4. The region R is bounded by the line hx � ry �3hr
� 0, y�
2h, the x -axis and the
y -axis. A conical frustum of radius of upper base r , radius of lower base 3r and height
2h is formed by rotating the region R through 2� about the y -axis. Show that the
volume of the conical frustum formed is
26
3
2
� rh.
[8]
[6]
[7]
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