# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#2

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**Question**

The diagram shows part of the curve and the point P(2,3) lying on the curve. Find, showing all necessary working, the volume obtained when the shaded region is rotated through 360^{o }about the x-axis.

**Solution**

Expression for the volume of the solid formed when the shaded region under the curve is rotated completely about the x-axis is;

Therefore, for the given case;

We are given that;

Hence, for x=0 and x=2;

Rule for integration of is:

Rule for integration of is:

Rule for integration of is:

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