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.

Answer 1

(i) Each side of square ABCD = 4 cm. 

∴ Area of Square: 

= (Side)²

= (4)² = 16 sq.cm. 

(ii) Area of circle in the corner A is 1 cm. 

Radius, r = 1 cm. 

θ = 90° 

∴ Area of quadrant of circle:

(iii) Radius of circle having diameter 2 cm, r = 1 cm. 

∴ Area of circle:

∴ Area of remaining part of Square : 

= Area of Square – Area of 4 quadrants – Area of Circle. 

= 16 – 4 × 0.78 – 3.14 

= 16 – 3.12 – 3.14 

= 16 – 6.26 

= 9.74 sq.cm.