OCR A Level: Core 3 - Volumes Of Revolution [January 2011 Q5]

The diagram shows the curve with equation $y= \dfrac{6}{\sqrt{3x-2}}$ . The region $R$ , shaded in the diagram, is bounded by the curve and the lines $x = 1,$ $x = a$ and $y = 0,$ where $a$ is a constant greater than 1. It is given that the area of $R$ is 16 square units.

Find the value of $a$ and hence find the exact volume of the solid formed when $R$ is rotated completely about the $x$ -axis.

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Input the nearest integer to the value of the volume as your answer.

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There are 9 marks available for this question.

In total, this question is worth 12.5% of all available marks in the paper.

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This is part of the set OCR A Level Problems .