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Areas Related to Circles
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section E - Case Study 1]
A circular brooch is made with silver wire in the form of a circle with diameter $35$ mm. The wire is also used in making $5$ diameters which divide the circle into $10$ equal sectors.
(i) Find the radius of the circular brooch. [1 Mark]
(ii) Find the total length of the silver wire required. [1 Mark]
(iii) (a) Find the area of each sector of the brooch. [2 Marks]
OR
(iii) (b) Find the central angle subtended by each sector at the centre. [2 Marks]
A circular brooch is made with silver wire in the form of a circle with diameter $35$ mm. The wire is also used in making $5$ diameters which divide the circle into $10$ equal sectors.
(i) Find the radius of the circular brooch. [1 Mark]
(ii) Find the total length of the silver wire required. [1 Mark]
(iii) (a) Find the area of each sector of the brooch. [2 Marks]
OR
(iii) (b) Find the central angle subtended by each sector at the centre. [2 Marks]
Step-by-Step Solution
Key Concept: Circle sector and perimeter calculations.
(i) $r = 35/2 = 17.5$ mm. [1.0 Mark]
(ii) Wire length $= \text{Circumference} + 5 \times \text{Diameter} = \pi(35) + 5(35) = \dfrac{22}{7} \times 35 + 175 = 110 + 175 = 285$ mm. [1.0 Mark]
(iii)(a) $\text{Area of sector} = \dfrac{1}{10} \times \pi r^2 = \dfrac{1}{10} \times \dfrac{22}{7} \times \dfrac{35}{2} \times \dfrac{35}{2} = \dfrac{385}{4} = 96.25$ mm$^2$. [2.0 Marks]
OR (iii)(b) Central angle $= \dfrac{360^\circ}{10} = 36^\circ$. [2.0 Marks]
(ii) Wire length $= \text{Circumference} + 5 \times \text{Diameter} = \pi(35) + 5(35) = \dfrac{22}{7} \times 35 + 175 = 110 + 175 = 285$ mm. [1.0 Mark]
(iii)(a) $\text{Area of sector} = \dfrac{1}{10} \times \pi r^2 = \dfrac{1}{10} \times \dfrac{22}{7} \times \dfrac{35}{2} \times \dfrac{35}{2} = \dfrac{385}{4} = 96.25$ mm$^2$. [2.0 Marks]
OR (iii)(b) Central angle $= \dfrac{360^\circ}{10} = 36^\circ$. [2.0 Marks]
Correct Answer: (i) 17.5 mm | (ii) 285 mm | (iii)(a) 385/4 mm² OR (iii)(b) 36°
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