Question 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.
Open in App
Solution
Given that, three circles are in such a way that each of them touches the other two now. We join centre of all three circles to each other by a line segment. Since, radius of each circlesis 3.5 cm,
So, AB=2×Radiusofcircle
=2×3.5=7cm
⇒AC=BC=AB=7cm
Which shows that, ΔABCis an equilateral triangle with side 7 cm.
We know that each angle between two adjacent sides of an equilateral triangle is 60∘.
∴Area of sector with angle ∠A=60∘
=∠A360∘×πr2=60∘360∘×π×(3.5)2
So, area of each sector = 3 × Area of sector with angle A
=3×60∘360∘×π×(3.5)2
=12×227×3.5×3.5
=11×510×3510=112×72
=774=19.25cm2
Area of ΔABC=√34×Side2 =√34×72=21.21
Area of the shaded region
= Area of the equilateral triangle - Area of three sectors
=21.2176−1925=1.9676cm2
Hence, the required area enclosed between these circles is 1.967cm2(approx)