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Three Equal Circles, Each of Radius 6 Cm, Touch One Another as Shown in the Figure. Find the Area of Enclosed Between Them. - Mathematics

Sum

Three equal circles, each of radius 6 cm, touch one another as shown in the figure. Find the area of enclosed between them.

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Solution

Join ABC. All sides are equal, so it is an equilateral triangle.
Now,
Area of the equilateral triangle `=sqrt(3)/4xx"Side"^2`

`= 1.73/4xx12xx12`

= 62.28 cm

Area of the arc of the circle`=60/360pi"r"^2`

`= 1/6pi"r"^2`

`=1/6xx22/7xx6xx6`

= 18.86 cm2

Area of the three sectors = 3 × 18.86 = 56.57 cm

Area of the shaded portion = Area of the triangle -- Area of the three quadrants

= 62.28 - 56.57

= 5.71 cm

  Is there an error in this question or solution?
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18B | Q 39 | Page 833
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