Question

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 ?

Answer 1

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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