CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1 · Question 36

Areas Related to Circles 4 marks Hard

The Olympic symbol comprising five interlocking rings represents the union of the five continents of the world and the meeting of athletes from all over the world at the Olympic games. The five circular rings of class-X took part in various activities organised by the school. One such group of students made

5

circular rings in the school lawn with the help of ropes. Each circular ring required

44

m of rope. Also, in the figure shaded regions as shown in the figure, students made rangoli showcasing various sports and games. It is given that

△ O A B

is an equilateral triangle and all unshaded regions are congruent. Based on above information, answer the following questions.

(i)Find the radius of the ring $R_{1}$ .[1]
(ii)What is the measure of $∠ A O B$ ?[1]
(iii)(a)Find the area of shaded region $R_{1}$ .[2]
(iii)(b)OR — Find the length of rope on the unshaded regions.[2]

Answer

(i) The radius of each ring is

7

m; (ii)

∠ A O B = 6 0^{\circ}

; (iii)(a) The shaded region has area

R_{1} = (\frac{308}{3} + \frac{49 3}{2}) m^{2} \approx 145.1 m^{2}

; (iii)(b) The rope around the unshaded regions is

\frac{176}{3} m \approx 58.67

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CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1 · Question 36

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