# 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."

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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 $378\ cm^2$.

Updated on 10-Oct-2022 13:24:15