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On a square handkerchief, nine circular designs each of the radius 7 cm are made (see figure). Find the area of the remaining portion of the handkerchief.
"
Given:
On a square handkerchief, nine circular designs each of the radius 7 cm are made.
To do:
We have to find the area of the remaining portion of the handkerchief.
Solution:
Radius of one circular design $= 7\ cm$
Area of one circular design $= \pi r^2$
$= \frac{22}{7} \times 7^2$
$= 154\ cm^2$
Area of 9 circular designs $= 9 \times 154$
$= 1386\ cm^2$
Diameter of the circular design $= 7 \times 2$
$= 14\ cm$
Side of the square $= 3\times$ Diameter of one circle
$= 3 \times 14$
$= 42\ cm$
Area of the square $= 42 \times 42$
$= 1764\ cm^2$
Area of the remaining portion of handkerchief $=$ Area of the square $-$ Area of 9 circular designs
$= 1764 - 1386$
$= 378\ cm^2$
The area of the remaining portion of the handkerchief is $378\ cm^2$.