Question

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

Answer 1

Radius of a circle $=7cm$

Length of side of the square $=3\left(14\right)=42cm$

Area of the square $=(side{)}^2={42}^2=1764c{m}^2$

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

Area of nine circles $=9\times 154=1386c{m}^2$

Remaining portion (without design) $=$ Area of handkerchief $-$ Area of design

$=1764-1386$

$=378c{m}^2$

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