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

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#### Solution

We have

r = 42 cm and θ = 360° - 90° = 270°

Perimeter of the top of the table = Length of the major arc AB + Length of OA + Length of OB

`=theta/360^circxx2pir+42+42`

`=270^circ/360^circxx2xx22/7xx42+84`

`=198 + 84`

= 282 cm

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

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