A sector with a given perimeter and area
A sector with a given perimeter and area
IP 2
7 marks
A sector of a circle has radius \(r\) cm and angle \(\theta\) radians, where \(0<\theta<2\pi\).
- The sector has perimeter \(30\) cm and area \(50\text{ cm}^2\). Find the two possible pairs of values of \(r\) and \(\theta\).[4]
- For any sector with perimeter \(30\) cm, show that its area is \(r(15-r)\text{ cm}^2\). Hence find the greatest possible area and the corresponding angle.[3]
Solution:
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Answer:(a) \(r=5\), \(\theta=4\) \(r=10\), \(\theta=1\) (b) \(56.25\text{ cm}^2\) at \(r=7.5\), \(\theta=2\) radians
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