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 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/π

=> Sector angle =  150/3.14 = 47.77°

Arc Length of Smaller Sector = 10 cm

=> 10  =  (  150/π*360) * 2 π Radius

=> Radius = 12 cm

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

= 30 + 24

= 54 cm

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