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  • Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

Answers (1)

1.966 cm2

Solution

Radius = 3.5

Diameter = 3.5 + 3.5 = 7 cm

 

Here ABC is equilateral triangle because AB = BC = CA = 7 cm

\thereforeArea of \triangle ABC=\frac{\sqrt{3}}{4}a^{2}

                                   \\=\frac{\sqrt{3}}{4} \times 7 \times 7\\ =\frac{49\sqrt{3}}{4}\\ =21.217 cm^{2}

In equilateral triangle each angle = 60°

All the sectors are same 

\therefore Area of all there sectors =3 \times \frac{\theta}{360^{\circ}} \times \pi r^{2}

                                               \\=3 \times \frac{60^{\circ}}{360^{\circ}} \times \frac{22}{7} \times (3.5)^{2}\\ =19.251 cm^{2}

Area of enclosed region = Area of DABC – Area of their sectors

                                        =21.217-19.251

                                        = 1.966cm2

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