OAB is a quadrant of a circle with OA (= OB) as its radius of length 4 cm. OA and OB are also diameters of two semi-circles as shown in the diagram below which is not drawn to scale. Shaded areas x and y are as shown in the diagram. What is the value of x y ?
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Given : OAB is a quadrant of a circle with OA (= OB) as its radius of length 4 cm.
OA and OB are also diameters of two semi-circles.
Shaded areas x and y are as shown in the diagram.
To Find : What is the value of x/y
Solution:
area of OAB = (1/4)π(4)² = 4π cm²
Area of one small semicircle = (1/2)π(2)² = 2π cm²
Area of 2 smaller semicircles = 2 * 2π = 4π cm²
Area of 2 smaller semicircles - x + y = area of OAB
=> 4π - x + y = 4π
=> x = y
=> x/y = 1
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