OCR C3 — Question 5

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
TopicVolumes of Revolution

5. The finite region \(R\) is bounded by the curve with equation \(y = \sqrt [ 3 ] { 3 x - 1 }\), the \(x\)-axis and the lines \(x = \frac { 2 } { 3 }\) and \(x = 3\).
  1. Find the area of \(R\).
  2. Find, in terms of \(\pi\), the volume of the solid formed when \(R\) is rotated through four right angles about the \(x\)-axis.