Answer: the perimeter of the shaded part is 15.978 cm
Step-by-step explanation:
The formula for determining the perimeter of a sector is expressed as
Length of arc + 2r
= θ/360 × 2πr + 2r
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
Considering the bigger sector,
θ = 50°
r = 8
Perimeter of the bigger sector is
(50/360 × 2 × 3.14 × 8) + (2 × 8)
= 6.978 + 16
= 22.978 cm
Radius of the smaller sector is
8 - 4.5 = 3.5 cm
Therefore, the perimeter of the shaded part would be
Perimeter of the bigger sector - 2(radius of the smaller sector). It becomes
22.978 - 2(3.5)
= 22.978 - 7
= 15.978 cm
