Question

three equal circles each of radius 2cm touch one another find the area enclosed between them

Answer 1

REFER TO ATTATCHMENT FOR YOUR ANSWER. .

Answer 2

The area enclosed between them would be 0.648 $cm^2$

Step-by-step explanation:

Given that,

Radius of each circle = 2cm

Since the radii of all the three triangles are the same and they are touching each other, it will form an equilateral triangle.

Construction: Join the radius of each triangle and make the triangle ABC.

This triangle comprises of the sectors of each triangle and since the triangle is equilateral, the area of the sectors would be equal.

So,

The area enclosed between = Area of the equilateral triangle - 3 × the area of a sector.

= $\frac{\sqrt{3} }{4} a^2 -$ 3 × θ/360° × πr^2

= $\frac{\sqrt{3} }{4}$ × 4 × 4 - 3 × 60°/360° × 22/7 × 2 × 2

= $4\sqrt{3}$ - 3 × 1/6 × 22/7 × 2 × 2

= $4\sqrt{3}$ - 3 × 88/42

= 6.928 - 3 × 2.095

= 0.648  $cm^2$

Thus, the area enclosed is 0.648 $cm^2$.

Learn more: Find the area

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