Question

The perimeter of a sector of a circle of radius 5.7cm and arclength 15.8cm is

Answer 1

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The perimeter of a sector of a circle of radius 5.7 cm and arc length 15.8 cm is

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Given:

Radius of a circle(OA,OB) = 5.7 cm

Perimeter of the sector of a circle= 27.2 cm

Let OAB be the given sector.

Perimeter of the sector OAB = 27.2 cm

OA + OB +Arc AB = 27.2 cm

5.7 +5.7 + Arc AB = 27.2

11.4 + Arc AB = 27.2 cm

Arc AB = 27.2 - 11.4 = 15.8 cm

Length of the sector AB(l)= 15.8 cm

Area of sector OAB = ½ le

= ½(15.8)(5.7) = 90.06 /2= 45.03 cm²

Hence, the Area of sector= 45.03 cm².

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