0

Given a circle of radius 9cm, and the length of the chord AB of a circle is 9√3 cm, find the area of the sector formed by arc AB.

**Comments**

0

Length of cord = 2r sin(θ/2)

where r is the radius

9√3 = 2r sin(θ/2)

9√3 = 2(9) sin(θ/2)

9√3 = 18sin(θ/2)

divide both sides by 18

9√3 / 18 = sin(θ/2)

√3 / 2 = sin(θ/2)

θ/2 = sin^{-1}(√3 / 2)

θ/2 = 60

multiply both sides by 2

θ = 120

Area of sector = 1/2 (Length of arc x radius)

Length of arc = θ/360 x 2πr

Area of sector = 1/2 (θ/360 x 2πr x r)

= θ/360 x πr^{2}

where r is the radius

Area of sector = 120/360 x π(9)^{2}

= 27π

But π = 22/7

Area of sector = 27 x 22/7

= 84.85 cm^{2}

Your Answer