Given Below Is The Picture of the Olympic Rings Made By Taking Five Congruent Circles of Radius 1Cm Each - Mathematics

Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm. Total area of all the dotted regions assuming the thickness of the rings to be negligible is



(a) 4(π/12-√3/4) cm²

(b) (π/6 - √3/4) cm²

(c) 4(π/6 - √3/4) cm²

(d) 8(π/6 - √3/4) cm² 

(d) 8(π/6 - √3/4) cm² 

Explanation:

Let the center of the circle is O.

OA = OB = AB =1cm.

So,

∆OAB is an equilateral triangle

∴ ∠AOB =60°

Required Area= 8x Area of one segment with radius=1cm, ∠O = 60°

Calculation for doted Area

= Area of Sector With angle 60° , Radius = 1 cm - Area of equilateral traingles with side 1 cm


= `\frac{\theta}{360^{0}}\times\pi r^{2}-\frac{\sqrt{3}}{4}a^{2}`

= `\frac{60^{0}}{360^{0}}\times\pi 1^{2}-\frac{\sqrt{3}}{4}1^{2}`

= `(\frac{\pi}{6}-\frac{\sqrt{3}}{4})cm^{2}`

= Area = 8 `\times` doted Area

=8 `\times` `(\frac{\pi}{6}-\frac{\sqrt{3}}{4})cm^{2}`

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CBSE Class 10 Mathematics Sample Paper-2022