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
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.
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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