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


Give:

Radius of the circle = 42 cm


Central angle of the sector = AOB = 90°


Perimeter of the top of the table = Length of the major arc AB + 2 × radius …………………. (i)


Length of major arc AB = × 2πr


= × 2 × × 42


= × 2 × 22 × 6


= × 264 = 3 × 66 = 198 cm


Thus, using (i), we have


Perimeter of the top of the table = 198 + 2 × 42


= 198 + 84 = 282 cm


Hence, the perimeter of the top of the table is 282 cm.


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