Question

If the area of a sector of a circle of radius 36 cm is 54π cm², then the length of the corresponding arc of the sector is ______.

पर्याय

• 8π cm

• 6π cm

• 4π cm

• 3π cm

Answer 1

If the area of a sector of circle of radius 36 cm is 54π cm², then the length of the corresponding arc of the sector is 3π cm.

Explanation:

Given:

Radius of the circle (r) = 36 cm

Area of the sector = 54π cm²

Area of a sector = `theta/360 xx pi r^2 = 54 pi`    ...(i)

Substituting r = 36 in equation (i)

Area of a sector = `theta/360 xx pi (36)^2 = 54 pi`

Area of a sector = `theta/360 xx 1296 pi = 54 pi`

Dividing both sides by π we get,

`theta/360 xx 1296 = 54`

`theta = (54 xx 360)/1296`

∴ θ = 15°

Arc length = `theta/360 xx 2 pi r`    ...(ii)

Substituting θ = 15° and r = 36 in equation (ii), we get,

Arc length = `15/360 xx 2 pi xx 36`

Arc length = `1/24 xx 72 pi`

Arc length = 3π cm