Question 13 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard [Term I] - Solutions of Sample Papers for Class 10 Boards

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Question 13 The area (in cm^2) of a sector of a circle of radius 21 cm cut off by an arc of length 22 cm is (A) 441 (B) 321 (C) 231 (D) 221Let the arc subtend an angle 𝜃 at the center Now, Length of Arc APB = 𝜃/360 × (2𝜋𝑟) 22 = 𝜽/(𝟑𝟔𝟎°) × 𝟐 × 𝟐𝟐/𝟕 × 𝟐𝟏 22 = 𝜃/(360°) × 2 × 22 × 3 22 × 360° × 1/(2 × 22 × 3)=𝜃 (𝟑𝟔𝟎° )/(𝟐 × 𝟐𝟐 × 𝟑) = 𝜃 60° = 𝜃 𝜃 = 60° Now, Area of required sector = 𝜃/360×𝜋𝑟2 = 𝟔𝟎/𝟑𝟔𝟎 × 𝟐𝟐/𝟕 × 𝟐𝟏 × 𝟐𝟏 = 1/6 × 22/7 × 21 × 21 = 1/6 × 22 × 3 × 21 = 231 cm2 So, the correct answer is (c)