Question : Calculate the area of a sector of a circle with a radius of 10 metres and an angle of 90 degrees at the centre.
Option 1: 79.3 m2
Option 2: 79.5 m2
Option 3: 78.5 m2
Option 4: 75 m2
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Correct Answer: 78.5 m 2
Solution :
Given $r$ = 10 m and $\theta$ = 90°
Area of a sector = $πr^2\times\frac{\theta}{360°}$
⇒ Area of the sector = $\frac{22}{7}\times 10^2\times \frac{90°}{360°}$
= $\frac{22}{7}\times 100\times \frac{1}{4}$
= 78.57 ≈ 78.5 m
2
Hence, the correct answer is 78.5 m
2
.
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