Areas related to Circles
Asked by RACHIT_MAHAAN | 18th Feb, 2010, 07:04: PM
Shaded area = area of quadrilateral ABDE - area of minor sector of 4cm circle, near shaded area - area of minor sector of 12 cm circle, near shaded area.
AB = 4 + 12 = 16 cm.
AE = CD = 4 cm
BC = BD - CD = 12 - 4 = 8 cm
cos B = BC/AB = 8/16 = 1/2
B = 60
Area of minor sector in 12 cm circle, near shaded area = (1/2)(π/3)(12)(12) = 24π
In quadrilateral ABDE, E = D = 90, B = 60 and hence A = 30.
Area of minor sector in 4 cm circle, near shaded area = (1/2)(π/6)(4)(4) = 4π/3
Area of quadrilateral, ABDE = Area of rectangle ACDE + Area of triangle ABC
= (AC)(AE) + (1/2)(AC)(BC)
= 83x4 + 0.5x83 x8 = 643 ...........AC = (AB2-BC2)
The shaded area = 643 - 4π/3 - 24π = 31.3 cm2
Answered by | 19th Feb, 2010, 06:47: AM
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