Question

3 For the diagram (right), calculate:
a the radius of the smaller sector,
b the perimeter of the shape,
c the angle 0.
20 cm
10 cm
- 24cm

Answer 1

Given:  

A diagram of sector with larger radius & smaller radius  

To find:

(a) the radius of the smaller sector.

(b) the perimeter of the shape

(c) the angle.

Solution:

Radius of Bigger sector  = 24 cm

Arc Length of Bigger Sector = 20 cm

Arc length =  (  Sector angle / 360° ) × 2 π Radius

⇒  20 =   (  Sector angle / 360° ) × 2 π   × 24

⇒ Sector angle =  7200 /48π

⇒ Sector angle =  150/3.14 = 47.77°

∴ (c) The angle = 47.77 °

Arc Length of Smaller Sector = 10 cm

⇒ 10  =  (  150/π × 360)  × 2 π rad

⇒ Radius = 12 cm

(a) The radius of the smaller sector is 12 cm

Perimeter of the shape = 20 + 10  + 2 ( 24 - 12 )

= 30 + 24

= 54 cm

(b) The perimeter of the shape is 54 cm

Therefore, we have,

(a) The radius of the smaller sector is 12 cm

(b) The perimeter of the shape is 54 cm

(c) The angle = 47.77 °