# 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 - Mathematics

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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#### APPEARS IN

NCERT Class 10 Maths
Chapter 12 Areas Related to Circles
Exercise 12.3 | Q 5 | Page 235