Question:
From each corner of a square of side 4cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2cm is cut from the centre of the square. Find the area of the remaining portion of the square.
Answer:
Each quadrant is a sector of 90° in a circle of 1 cm radius.
Now, area of the each quadrant = (90/360) * πr2
= (1/4)* (22/7)*1
= 22/28
= 11/14 cm2
Again, area of the square = (side)2 = 42 = 16 cm2
and area of the circle = πr2 = (22/7) * 1 = 22/7 cm2
Now, area of the remaining portion = Area of the square - (area of the circle + 4 * area of the quadrant)
= 16 - (22/7 + 4 * 11/14)
= 16 - (22/7 + 2 * 11/7)
= 16 - (22/7 + 22/7)
= 16 - 44/7
= (16*7 - 44)/7
= (112 - 44)/7
= 68/7 cm2
So, area of the remaining portion is 68/7 cm2
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