50
Paper 1 – Volumes of Revolutions
11
Example
R is defined to be the region bounded by the curve
1 y � and the lines
� sin x 2
1 x � ,
3 x � 1 and the x -axis.
( a ) Find the area of R .
R is rotated through 2π radians about the x -axis to form a solid .
( b ) Find the volume of the solid generated .
[ 2 ]
[ 2 ]
Solution
( a ) The area of R
1 1 � � 1 dx ( A1 ) for correct approach
�
3 sin x 2
� 0.8384014366 � 0.838
A1
( b ) The volume of the solid
2
|
�
� 1 � 1
� � �
1�
�
�
� 3 �sin x
� � 2
�
|
dx |
( A1 ) for correct approach |
|
�
3.464101615
|
|
|
|
�
3.46
|
|
A1 |
[ 2 ]
[ 2 ] www . seprodstore . com
179