CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
Last updated at April 16, 2024 by Teachoo
Question 37 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/12ββ3/4) cm2 (b) (π/6ββ3/4) cm2 (c) 4 (π/6ββ3/4) cm2 (d) 8 (π/6ββ3/4) cm2 Letβs consider only one circle In Ξ OAB, all sides are equal β΄ Ξ OAB is an equilateral triangle So, all angles are 60Β° Area of red shaded region = Area of sector with angle 60Β° and radius 1 cm β Area of equilateral triangle with side 1 cm = ΞΈ/(360Β° ) Γ πr2 β β3/4 π^2 = (ππΒ° )/(πππΒ° ) Γ π (1)2 β βπ/π (1)2 = ( π/(π ) β βπ/π ) cm2 Now, Required Area = 8 Γ Area of red portion = 8 Γ ( π/(π ) β βπ/π ) cm2 So, the correct answer is (d)
