Question

If the adjoining figure is a sector of a circle of radius 10.5 cm, what is the perimeter of the sector? (Take $(\pi=\frac{22}{7})$)​

Answer 1

Answer:

The perimeter of the sector is 32 cm.

Step-by-step explanation:

Given :  

Radius of a circle, r = 10.5 cm

Angle subtended by an Arc at the centre of a circle,θ = 60°

Perimeter of the sector ,P = length of the arc, AB + radius, AC + radius, BC

P = θ/360° × 2πr + r + r  

P = θ/360° × 2πr + 2 r  

P = 60°/360° × 2 × π× 10.5 + 2 × 10.5  

P = ⅙×21π + 21  

P = 21π/6 + 21

P = 21 × 22/7 × ⅙ + 21

P = 22/2 + 21

P = 11 + 21

P = 32 cm

Perimeter of the sector = 32 cm

Hence, the perimeter of the sector is 32 cm.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Step-by-step explanation:

Perimeter of the sector =AC+BC+arc AB

AC=BC=radius=10.5 cm

Length of the arc of the sector with central angle, θ (in degree) is =

360

θ

×2πr

So, length of the arc AB=

360

60

×2π×(10.5)

=

3

1

×

7

22

×(10.5)

=11 cm

Perimeter of the sector =10.5+10.5+11=32 cm.