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

Calculus Level 4

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.

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

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