Question : The perimeter of a sector of a circle is 24 cm and the radius is 3 cm. Calculate the area (in cm2 ) of the sector.
Option 1: 24
Option 2: 33
Option 3: 27
Option 4: 30
Correct Answer: 27
Solution :
Given: The perimeter of a sector of a circle = 24 cm
Radius = 3 cm
Perimeter of the sector = (2 × radius) + length of the arc
⇒ 24 = (2 × 3) + length of the arc
⇒ Length of the arc = 18
We know that,
Area of the sector $=\frac{1}{2}lr=\frac{1}{2}\times18\times3= 27$ cm
2
Hence, the correct answer is 27.
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