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What will be the perimeter of the top of the table, if in the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $∠ A O B = 90 ° .$ , with AOB=42 cm?

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280 cm

282 cm

284 cm

285 cm

answer is B.

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Detailed Solution

Given,

∠ A O B = 90 ° .

, with AOB=42 cm.
We have to find the perimeter of the top of the table.
Calculating the perimeter of the top of the table,
Length of the arc

= 2 π r θ 360 °

The perimeter of the top of the table = (Length of the major arc AB) + (Length of OA) + (Length of OB)

= θ 360 ° × 2 π r + 42 + 42 = 270 ° 360 ° × 2 × 227 × 42 + 84 = 198 + 84 = 282 cm

So, the perimeter of the top of the table is 282 cm.
Therefore, option 2 is correct.

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