Question

the boundary of the shaded region is given figure consists of three semicircles the smaller begin equal if the diameter of the larger one is 28 cm find ( 1 )the length of the boundary (2) the area of the shaded region ,,,, plz ans it correctly I will mark as brainliest answer ​

Answer 1

(1) 31.4 cm

(2) 39.25 cm²

Step-by-step explanation:

From figure:

⇒ Diameter of larger arc = AB = 10 cm.

⇒ Diameter of smaller arc = AC = BC = 5 cm.

(i) Length of boundary:

= Length of semicircle ADB + Length of semicircle BEC + Length of semicircle AFC

= [1/2 π (10) + 1/2 π (5) + 1/2 π(5)]

= [5π + 10π/2]

= [5π + 5π]

= 10π

= 10 * 3.14

= 31.4 cm.

(ii) Area of shaded region:

Area of semi-circle ADB - Area of semicircle AFC + Area of semicircle BEC

= [1/2 * π * (5)² - (1/2) * π * (2.5)² + (1/2) * π * (2.5)²]

= [1/2 * π * 25]

= [25π/2]

= 39.25 cm²

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