Question

In the given figure, 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
three circles. ​

Answer 1

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Answer 2

Correct question:-

In the given figure, 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

three circles. ( Shaded portion )

$\huge\sf\underline{\underline{Solution:}}$

▪Given that:-

• Radius of three circles = 3.5cm ,are drawn in such a way that each of them touches the other two.

▪To find:-

• The area enclosed between these three circles.

___________________________________

•Construction:- Draw a line connecting the centres of each pair of adjacent circles creating a equilateral triangle of side length 7 cm.

Now,

Area of triangle =

$\sf \dfrac{ \sqrt{3} }{4}\times{(side)}^{2}\\ \\ \sf \dfrac{\sqrt{3} }{4} \times{7}^{2}\\ \\ \sf \frac{49 \sqrt{3}}{4}$

There are four areas inside of this equilateral triangle.

[Three 60° circle sector.]

Area of sector =

$\frac{?}{360} \pi \: r {}^{2} \\ \\ = \frac{60}{360} \times \frac{22}{7} \times ( \frac{7}{2} ) {}^{2} \\ \\ = \frac{77}{12} cm {}^{2}$

Area of three sectors = $\frac{77}{4}cm^2$

Thus, area of Shaded portion = area of equilateral triangle - area of three sectors

$\frac{49 \sqrt{ 3} }{4} - \frac{77}{4} = 1.97cm {}^{2}$

$\sf\huge\boxed{1.97}$