The design is from two sectors of circles, centre o. Calculate the perimeter of the shaded part. Give your answer correct to 3 significant figures.

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

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