Question

a sector is cut-off from a circle of a radius 21 cm. the angle of a sector is 120°. find the length of its arc and the area.​

Answer 1

EXPLANATION.

• GIVEN

area of sector is cut off from a circle of a radius

21 cm

the area of a sector is 120°

TO FIND THE LENGTH OF IT'S ARC AND THE AREA.

Let radius of a circle ( r) = 21 cm

ø = angle suspend to the centre = 120°

Formula of it's length of arc,

$\frac{ \theta}{360} \times 2\pi \: r$

$\frac{120}{360} \times 2 \times \frac{22}{7} \times 21$

Length of arc = 44 cm

Formula of area of sector,

$\frac{ \theta}{360} \times \pi {r}^{2}$

$\frac{120}{360} \times \frac{22}{7} \times 21 \times 21$

$22 \times 21$

area of sector = 462cm^2

Therefore,

Length of arc = 44 cm

Area of sector = 462 cm^2

Answer 2

Answer:

The length of the arc is 44 cm & Area of sector of a circle is 462 cm².

Step-by-step explanation:

Given :

Radius of circle,r = 21 cm

Angle subtended by an arc, θ = 120°

 

Length of the arc, l = (θ/360) × 2πr

l =  (120°/360°) × 2π × 21

l = 1/3 × 2 × 22/7 × 21

l = (44 × 7)/7

l = 44 cm

Length of the arc, l = 44 cm  

 

Area of the sector of a circle, A = (θ/360) × πr²

A = (120°/360°) × π ×21²

A = ⅓  × 22/7 × 21 × 21

A = 22 × 7 × 3

A = 154 × 3

A = 462 cm²

Area of sector of a circle ,A = 462 cm²

Hence, the length of the arc is 44 cm & Area of sector of a circle is 462 cm².