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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

100 cm2

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B

346 cm2

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C

178 cm2

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D

378 cm2

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Solution

## The correct option is D 378 cm2 Number of circular design = 9 Radius of the circular design = 7 cm There are three circles on one side of the square handkerchief. ∴ Side of the square =3×diameter of circle=3×14=42 cm Area of the square =42×42 cm2=1764 cm2 Area of the circle =πr2=227×7×7=154 cm2 Total area of the design =9×154=1386 cm2 Area of the remaining portion of the handkerchief = Area of the square - Total area of the design =1764−1386=378 cm2

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