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Three circles each of radius $7 cm$ are drawn in such a way that each of them touches the other two. Find the area enclosed between the circles.

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5 c m^{2}

9 c m^{2}

7.86 c m^{2}

10 c m^{2}

answer is A.

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Detailed Solution

Given that, the circles each of radius 7 cm are drawn in such a way that each of them touches the other two.
We know that, the area of equilateral triangle is

34 a 2

and the area of sector is

0 360 ° π r 2

Calculating the area of equilateral triangle which is formed when the centre of three circles are joined,

34 a 2 = 34142

⇒ 34 × 196

\Rightarrow

3 cm

Calculating the area of sector,

3 × θ 360 ° π r 2 ⇒ 3 × 60 ° 360 ° π 72

⇒ 3 × 16 × 227 × 72

\Rightarrow

{cm}^{2}

Finding the area of the enclosed region by subtracting the area of sector from the area of equilateral triangle,

493 − 77 = 7.86 c m 2

Therefore, area enclosed between the circles is 7.86

{cm}^{2}

.
Hence the correct option is 1.

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