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Question
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the given figure. Find the area of the remaining portion of the square [Use Π = 22/7]
Solution
Each quadrant is a sector of 90° in a circle of 1 cm radius.
Area of each quadrant = `90^@/360^@pir^2`
`= 1/4xx22/7xx(1)^2 = 22/28 cm^2`
Area of square = (Side)2 = (4)2 = 16 cm2
Area of circle = πr2 = π (1)2
`= 22/7 cm^2`
Area of the shaded region = Area of square − Area of circle − 4 × Area of quadrant
` = 16 -22/7 - 4 xx 22/28`
`= 16-22/7-22/7 = 16 - 44/7`
`= (112-44)/7 = 68/7 cm^2`
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