Question

On a square handkerchief, nine circular designs each of radius 7 cm are made (see the Figure). Find the area of the remaining portion of the handkerchief.

Answer 1

(i) Total area of 9 circular designs each of radius 7 cm

(ii) All the circles touches externally. 

∴ Sum of the diameter of 3 circles in first Row 

= 14 + 14 + 14 = 42 cm. 

∴ Length of each side of square ABCD, 

a = 42 cm. 

∴ Area of square ABCD = a² 

= (42)² = 1764 sq.cm. 

Area of remaining part of handkerchief: 

= Area of square – Area of 9 circles. 

= 1764 – 1386 

= 378 sq.cm.