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. [CBSE 2012]

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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
$= \frac{θ}{360^{°}} \times 2 π r + 42 + 42 = \frac{270 °}{360 °} \times 2 \times \frac{22}{7} \times 42 + 84 = 198 + 84 = 282 cm$

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

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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. [CBSE 2012]

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 =θ360°×2πr+42+42=270°360°×2×227×42+84=198+84=282 cm Hence, the perimeter of the top of the table is 282 cm.