CAIE P1 2011 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
TopicVolumes of Revolution

8 The equation of a curve is \(y = \sqrt { } \left( 8 x - x ^ { 2 } \right)\). Find
  1. an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), and the coordinates of the stationary point on the curve,
  2. the volume obtained when the region bounded by the curve and the \(x\)-axis is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.