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

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278 {cm}^{2}

288 {cm}^{2}

388 {cm}^{2}

378 {cm}^{2}

answer is D.

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Detailed Solution

Given,
Radius

r = 7 cm

Diameter of circular design d = 2r
The square side (s) = 3

\times d

= 3 (2 r

)

= 3 (2 \times 7)

= 42 cm

Calculate the area of the square handkerchief

=

Side

\times

Side

= 42 \times 42

= 1764 {cm}^{2}

Now, we calculate the area of one circular design

= π r^{2}

= \frac{22}{7} \times 7^{2}

= 154 {cm}^{2}

So, the area of nine circles we have

= 9 \times 154

= 1386 {cm}^{2}

Now, we have using the following method to gain remaining portion of the handkerchief area,
Area of square – Area of nine circle

= 1764 - 1386

= 378 {cm}^{2}

Option 4 is correct.

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