# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#3

**Question**

A sector of a circle of radius cm has an area of cm^{2}. Express the perimeter of the sector in terms of and .

**Solution**

We are given that for the circular sector;

We are required to find expression for perimeter of the circular sector.

Expression for perimeter of a circular sector with radius and angle rad is;

Therefore, for the given circular sector;

Hence, we need arc length of circular sector.

Expression for length of a circular arc with radius and angle rad is;

Therefore;

We are not given angle rad. We need to find angle rad.

Expression for area of a circular sector with radius and angle rad is;

Therefore, for the given case;

Hence;

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