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What will be the area of the shaded region, if ABCD is a square of side 14 cm and all circles are of the same diameter?

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45 cm 2

46 cm 2

42 cm 2

48 cm 2

answer is C.

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Detailed Solution

We have to find the area of the shaded region, if ABCD is a square of side 14 cm and all circles are of the same diameter.
Question Image

Calculating the area of the square,
Area of the square,

= (s i d e) 2 = 142 = 196 cm 2

Calculate the area of all the circles,
Area of the circles,

= π r 2

= 4 × π × 3.5 × 3.5 = 4 × 227 × 3.5 × 3.5 = 154 cm 2

Calculating the area of the shaded region,
Area of the shaded region = Area of the square - Area of four circles

= 196 − 154 = 42 cm 2

So, the area of the shaded region is

42 cm 2

.
Therefore, option 3 is correct.

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