In the given figure, three sectors of a circle of radius 5 cm, making angles $35°$, $50°$ and $95°$ at the centre are shaded. Find the area of the shaded region. [Use $\pi = \frac{22}{7}$]

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Question

In the given figure, three sectors of a circle of radius 5 cm, making angles $35°$, $50°$ and $95°$ at the centre are shaded. Find the area of the shaded region. [Use $\pi = \frac{22}{7}$]

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Accepted Answer

Step 1: Area of shaded region $= \frac{35}{360} 	imes \frac{22}{7} 	imes (5)^2 + \frac{50}{360} 	imes \frac{22}{7} 	imes (5)^2 + \frac{95}{360} 	imes \frac{22}{7} 	imes (5)^2$
Step 2: $= \frac{(35 + 50 + 95)}{360} 	imes \frac{22}{7} 	imes (5)^2 = \frac{180}{360} 	imes \frac{22}{7} 	imes 25 = \frac{1}{2} 	imes \frac{22}{7} 	imes 25$
Step 3: $= \frac{550}{14} \approx 39.29$ cm$^2$

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