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
Solution:
Given, three circles with a radius 3.5 cm each are drawn in such a way that each of them touches the other two.
We have to find the area enclosed between these circles.
From the figure,
Three circles with centre A, B and C are drawn.
Joining the centres A, B and C forms a triangle.
AB = BC = AC = 3.5+3.5 = 7 cm
So, ABC is an equilateral triangle with sides equal to 7 cm.
Area of the equilateral triangle = (√3/4)a²
= (√3/4)(7)²
= (√3/4)(49)
= 21.218 cm²
Central angle of each sector, θ = 60°
Radius = 3.5 cm
Area of sector = πr²θ/360°
= (22/7)(3.5)²(60°/360°)
= (22/7)(3.5)²(1/6)
= 6.417 cm²
Area of 3 sectors = 3(6.417)
= 19.25 cm²
Area enclosed between three circles = area of equilateral triangle - area of 3 sectors.
= 21.218 - 19.25
= 1.968 cm²
Therefore, the area enclosed between three circles is 1.968 cm².
✦ Try This: Three circles each of radius 7.3 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 7
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
Summary:
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. The area enclosed between these circles is 1.968 cm²
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