Question

the boundary of the shaded portion consists of 2 semicircles. diameter of the circle with center O is 28 cm. AQ=1/4AB. find the area of the shaded portion

Answer 1

Answer:

Step-by-step explanation:

Length of AB = 28 cm

Length of AQ = 1/4 of AB = 1/4 * 28 = 7 cm

Length of QB = Length of AB - AQ = 28 cm - 7 cm = 21cm

Area of circle = pie*r^2

⇒Area of semi-circle = 1/2 pie*r^2 = pie*r^2/2

radius of semi-circle 1 (the one whose diameter is AQ) = diameter/2 = 7/2 = 3.5 cm

radius of semi-circle 2 (the one whose diameter is QB) = 21/2 = 10.5 cm

Area of  semi-circle 1 = pie*r^2/2 = 3.14*3.5/2 = 10.99/2 = 5.495 cm^2

Area of semi-circle 2 = pie*r^2/2 = 3.14*10.5/2 = 32.97/2 = 16.485 cm^2

⇒Hence, area of shaded region = area of semi-circle 1 + semi-circle 2 = 5.495 + 16.485 = 21.98 cm^2

Hence the srea of shaded region is 21.98 cm^2.

Hope it helps.

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