Question

On a square handkerchief, nine circular designs each of radius$7$ cm are made (see the given figure). Find the area of the remaining portion of the handkerchief. $[\text{Use}\pi =\frac{22}{7}]$

Answer 1

Area of the remaining portion $=$ Area of square $-$ Area of $9$ circles.

Here, the handkerchief is made up of contributing $9$ circles.

So, side of the square $=3\times$ Diameter of circle

Here, the radius of a circle is $7cm$

$\therefore$ Diameter of circle is $14cm$

$\Rightarrow$side of a square $=3\times 14=42cm$

$\therefore$ Area of the square $=42\times 42=1764c{m}^2$

Area of one circle

$=\pi r^2=\frac{22}{7}\times 7^2=154c{m}^2$

Hence area of $9$ circles

$=9\times 154=1386c{m}^2$

$\therefore$ Area of the remaining portion $=$ Area of square $-$ Area of $9$ circles.

$=1764-1386$

$=378c{m}^2$

Hence, area of the remaining portion is $378c{m}^2$