Find the area of the shaded region.
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Answers
Answer:
Area of the shaded region = 865.4625 cm²
Step-by-step explanation:
In this we have to find the area of 3 semi-circles (2 small and 1 large)
Let a, b are the radius of two small semi-circle
and c is the radius of 1 large semi-circle
Let d1, d2, and, d3 are the diameters of 2 small semi-circle and 1 large semi-circle respectively.
Diameter of all the three circles is given.
We have to find the radius.
Radius = diameter / 2
d1 = 21 cm. So, a = 21/2 = 10.5 cm
d2 = 21 cm. So, b = 21/2 = 10.5 cm
d3 = 42 cm. So, c = 42/2 = 21 cm
Area of a semi-circle = πr² / 2
Area of two semi-circles with radius equals to 10.5 cm is,
π × (10.5)² / 2
Take π = 3.14
Area = (3.14 × 110.25) / 2 = 346.185/2 = 173.0925 cm²
∴ Area of two semi-circles with radius equals to 10.5 cm = 173.0925 cm²
Area of semi-circle with radius equals to 21 cm is,
Area = π × (21)² / 2
= (3.14 × 441) / 2 = 1384.74/2 = 692.37 cm²
∴ Area of semi-circle with radius equals to 21 cm = 692.37 cm²
Area of the shaded region = Area of two semi-circles with radius equals to 10.5 cm + Area of semi-circle with radius equals to 21 cm
= (173.0925 + 692.37)cm² = 865.4625 cm²
∴ Area of the shaded region = 865.4625 cm²