BOD is the diameter of the semicircle with centre o
OD is the diameter of smaller semicircle
AB and CE are arcs of two quadrants with different
radii. If OD = 10 cm and AE = BC = 3 cm, find
(i) the perimeter,
(ii) the area,
of the shaded region.
Answers
Given : BOD is the diameter of the semicircle with centre o
OD is the diameter of smaller semicircle
AB and CE are arcs of two quadrants with different
radii. If OD = 10 cm and AE = BC = 3 cm,
To Find :
(i) the perimeter,
(ii) the area, of the shaded region.
Solution:
Radius of Larger Circle = 10 cm
Radius of Smaller circle = 10/2 = 5 cm
Radius of arc CE = 10 - 3 = 7 cm
area of the shaded region = Area of Larger semi circle + Area of smaller semicircle + Area (arc AB) - area (arc CE)
Area of Larger semi circle = (1/2)π10² = 50π cm²
Area of smaller semi circle = (1/2)π5² = 12.5π cm²
Area (arc AB) = (1/4) π10² = 25π cm²
Area (arc CE) = (1/4) π5² = 12.25π cm²
area of the shaded region = 50π + 12.5π + 25π - 12.25π
= 75.25π cm²
using π = 22/7
= 236.5 cm²
Perimeter = semi circle of Larger circle + Arc AB + arc CE + AE + CO + semi circle of smaller circle
= 10π + (1/2) 10π + (1/2) 7π + 3 + (10 - 3) + 5π
= 23.5π + 10 cm
= 83.85 cm
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Area = 236.5cm²
Perimeter = 83.85cm