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What will be the area of the sector, if the perimeter of a certain sector of a circle of radius 6.5 cm is 31?

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59.5 cm 2

57.5 cm 2

58.5 cm 2

56.5 cm 2

answer is C.

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Detailed Solution

We have to find the area of the sector, if the perimeter of a certain sector of a circle of radius 6.5cm is 31.
Question Image

Suppose O is the centre of the circle with a radius of 6.5 cm and OACBO be its sector with a perimeter of 31 cm.
Note that,

O A + O B + arc A B = 31 cm

Putting the values,

⇒ 6.5 + 6.5 + arc A B = 31 ⇒ arcAB = 31 − 13 ⇒ arc A B = 18 cm

Area of a sector

= 12 × Radius × Arc

Calculating the area of the sector,
Area of the sector OACBO,

= 12 × Radius × Arc = 12 × 6.5 × 18 = 58.5 cm 2

So, the area of the sector is

58.5 cm 2

.
Therefore, option 3 is correct.

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