Ab and cd are two diameters of a circle with centre o which are perpendicular to each other b is a diameter of the smaller circle if a is equals to zero find the area of the region
Answers
AB and CD are the diameters of a circle with centre O.
OA = OB = OC = OD = 7 cm (Radius of the circle)
Area of the shaded region
= Area of the circle with diameter OB + (Area of the semi-circle ACDA - Area of ACD)
Given:
Radius of larger circle,(OA) R = 7 cm
Diameter of smaller circle,(OD) = 7 cm
Radius of smaller circle = 7/2 cm
Height of ΔBCA( OC) = 7 cm
Base of ΔBCA ( AB )= 14 cm
Area of ΔBCA = 1/2 × base × height
Area of ΔBCA = 1/2 × AB × OC = 1/2 × 7 × 14 = 49 cm²
Area of larger semicircle with radius (OA)7 cm = 1/2 ×π ×7²= 1/2 ×22/7 ×7×7 = 77 cm²
Area of smaller circle with radius 7/2 cm = πr²= 22/7 × 7/2 × 7/2 = 77/2 cm²
Area of the shaded region =Area of smaller circle with radius 7/2 cm +Area of larger semicircle with radius 7 cm - Area of ΔBCA
Area of the shaded region = 77/2 + 77 - 49= 77/2 + 28 = (77 +56) /2= 133/2
Area of the shaded region = 66.5 cm²
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Hope this will help you....