Question

On a square handkerchief, nine circular designs each of radius 7 cm are made.find the area of the remaining portion of the handkerchief?

Answer 1

The circles will be 3×3 arrangement as it is a square.
So side of square = 3× diameter
= 6r = 6*7 = 42 cm
Area of square = 42*42

Area of 9 circles =9* pi r^2
= 9* 22/7 * 7*7
= 9*7*22

Remaining area = area of square - area of circles
= 42*42 - 9*7*22
= 126( 28 - 11)
= 126*17
= 2142 cm^2

Answer 2

First of all,

Let's find the side of the square:

Radius of one circle = 7cm

Diameter of one circle = 14 cm

Total circles in one side of the square = 3

So,

Side of the square = 14×3 = 42cm

Now,

Let's find the area of the remaining position:

Area of the remaining portion:-

= Area of the square - Area of 9 circles

= (side)² - 9πr²

= (42)² - 9×22/7×7×7

= 1764 - 198×7

= 1764-1386

= 378 cm²

Hence, the area of the remaining portion is 378 cm².