In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\angle AOB = 90°$. If $AO = OB = 42$ cm, then find the perimeter of the top of the table.

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Question

In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\angle AOB = 90°$. If $AO = OB = 42$ cm, then find the perimeter of the top of the table.

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Accepted Answer

Step 1: Reflex $\angle AOB = 360° - 90° = 270°$
Step 2: Perimeter of the top of table $=$ length of major arc $+ 2 	imes$ radius $= \frac{270}{360} 	imes 2 	imes \frac{22}{7} 	imes 42 + 2 	imes 42$
Step 3: $= 198 + 84 = 282$ cm

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