AQA C3 2005 June — Question 6

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2005
SessionJune
TopicVolumes of Revolution

6
    1. Sketch the graph of \(y = 4 - x ^ { 2 }\), indicating the coordinates of the points where the graph crosses the coordinate axes.
    2. The region between the graph and the \(x\)-axis from \(x = 0\) to \(x = 2\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis. Find the exact value of the volume of the solid generated.
    1. Sketch the graph of \(y = \left| 4 - x ^ { 2 } \right|\).
    2. Solve \(\left| 4 - x ^ { 2 } \right| = 3\).
    3. Hence, or otherwise, solve the inequality \(\left| 4 - x ^ { 2 } \right| < 3\).