Question

The central angle of a sector of circle of area 9π sq. cm is 60°, the perimeter of the sector is ______.

Options

• π

• 3 + π

• 6 + π

• 6

Answer 1

The central angle of a sector of circle of area 9π sq. cm is 60°, the perimeter of the sector is 6 + π.

Explanation:

Given - Area of circle = 9π sq. cm, θ = 60°

Area is 9π sq. cm

∴ πr² = 9π

∴ r² = 9

∴ r = 3 cm

`theta^c = 60^circ = (60 xx pi/180)^c = pi/3`

Length of arc ⇒ s = rθ

⇒ s = `3 xx pi/3`

⇒ s = π

Perimeter of sector = 2(r) + s

= 2(3) + π

= 6 + π