Math, asked by aditigpt96gmailcom, 23 days ago

In the figure given below, the boundary of the shaded region consists of semicircular arcs. The area of the shaded portion is 14 (a) 616 cm² (b) 385 cm² (c) 231 cm² (d) 308 cm²

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Answers

Answered by sattwikswain08
1

Answer:

Here's your answer

Step-by-step explanation:

Diameter of biggest semi circle = 14cm.

Diameter to two small semi circle = 3.5cm. Diameter of other semi circle= 14-(2×3.5) =

7cm.

Area of biggest semi circle = 1/2×(pi)×7^2 cm^2.

Area of two small semi circle= = (pi)x1.75^2 cm^2. Area of other semi circle = 1/2*(pi)x3.5^2

cm^2.

Area of shaded region= = (pi)x(24.5-3.0625+12.25) = (pi)x27.5625 cm^2= 86.59 cm^2.

Hope it helps

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Answered by clementcherian
1

Answer:

Step-by-step explanation:

1. Length of the boundary

Length of the boundary=perimeter of semi circle with diameter AB boundary of semi circle with diameter 7cm

Length of boundary =(π×7+π×3.5)+π×1.75+π×1.75

Length of boundary =π(7+3.5+1.75+1.75)

                                 =44cm

∴ The length of the boundary is 44cm.

2.Area of shaded region =

Area of largest semicircle + Area of medium semicircle-2 (Area of small semicircle )

Area=  

7

22

×  

2

7×7

+  

7

22

×  

100

35

×  

2

35

−2(  

7

22

−  

100×100

175×175

)

=77+19.25−2(481)

=96.25−9.62

=86.63cm  

2

 

Area of shaded region =86.63cm  

2

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