For the diagram, calculate: (a) the radius of the smaller sector. (b) the perimeter of the shape (c) the angle.
Answers
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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