Ex 12.3, 11
On a square handkerchief, nine circular designs each of radius 7 cm are made (see figure). Find the area of the remaining portion of the handkerchief.
Area of remaining portion
= Area of square Area of 9 circles
Here, handkerchief is made up of contributing 9 circles.
So, Side of square = 3 Diameter of circle
Here,
Radius of circle = 7 cm
Diameter of circle = 7 2 = 14 cm
So, Side of square = 3 14
= 42 cm
Area of square = (side)2
= (42)2
= 42 42
= 1764 cm2
Area of one circle = 2
= (7)^2
= 22/7 7 7
= 22 7
= 154 cm2
Area of 9 circles = 9 Area of one circle
= 9 154
= 1386 cm2
Area of remaining portion = Area of square Area of 9 circles
= 1764 1386
= 378 cm2
Hence, Area of remaining portion = 378 cm2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.