Question

On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

• A. $100c{m}^2$
• B. $346c{m}^2$
• C. $178c{m}^2$
• D. $378c{m}^2$

Answer 1

The correct option is D

$378c{m}^2$

Number of circular design = 9
Radius of the circular design = 7 cm
There are three circles on one side of the square handkerchief.
$\therefore$ Side of the square $=3\times diameterofcircle=3\times 14=42cm$
Area of the square $=42\times 42c{m}^2=1764c{m}^2$
Area of the circle $=\pi r^2=\frac{22}{7}\times 7\times 7=154c{m}^2$
Total area of the design $=9\times 154=1386c{m}^2$
Area of the remaining portion of the handkerchief = Area of the square - Total area of the design
$=1764-1386=378c{m}^2$