Q94 · Practice questionComplex familiar6 marks
QUESTION 94 (6 marks)
The region bounded by , and is rotated about the -axis.
a)[2 marks]
Express the boundaries using as a function of .
b)[4 marks]
Determine the exact volume of the solid formed.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
(a) , ; (b) .
Worked solution
(a) The curve becomes . The vertical limits are , and the region has .
(b) A washer perpendicular to the -axis has outer radius and inner radius . Hence
Rewrites the boundary and determines limits.
Forms the washer model.
Integrates correctly.
Obtains the exact volume.
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