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45 votes
45 votes
OAB is a sector of a circle with centre O and radius 7 cm.

7 cm
O
7cm
B
The area of the sector is 40 cm²
Calculate the perimeter of the sector.
Give your answer correct to 3 significant figures.

User Mousius
by
3.2k points

1 Answer

23 votes
23 votes

The perimeter of the sector of the circle is determined to be 28.428 cm.

The area of the sector is given as 40 cm² and the radius of the given circle is mentioned as 7 cm.

In order to calculate the perimeter we need to find the value of the angle of the sector and the arc length as well.

Area of the sector = angle of the sector/ 360° × πr²

⇒ 40 = x/360° × 22/7 × (7)²

⇒x = 40 × 360/ 22 × 7

⇒x = 93.506°

Arc length = angle of the sector/360° × π × 2 × r

Arc length = 93.506°/360° × 22/7 × 2 × 7 = 11.428 cm

∴ Perimeter = arc length + radius +radius

Perimeter = 11.428 + 7 + 7 = 28.428 cm

User Enpith
by
2.9k points