CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
Last updated at Oct. 3, 2024 by Teachoo
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Question 30 (A) The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutesGiven cosθ+sinθ=1 Squaring both sides (cosθ+sinθ )^2=1^2 〖𝒄𝒐𝒔〗^𝟐𝜽+〖𝒔𝒊𝒏〗^𝟐𝜽+2 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃=1 Putting 〖𝑐𝑜𝑠〗^2𝜃+〖𝑠𝑖𝑛〗^2𝜃 = 1 𝟏+2 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃=1 2 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃=1−1 2 𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃=0 𝒄𝒐𝒔𝜽 𝒔𝒊𝒏𝜽=𝟎 Between 7:05 p.m. to 7:40 p.m , The minute hand sweeps 35 minutes Let’s find angle swept Angle swept by minute hand in 1 hour (i.e. 60 minutes ) = 360° Angle swept by minutes hand in 1 minute = (𝟑𝟔𝟎°)/𝟔𝟎 Angle swept by minute hand in 35 minutes = (𝟑𝟔𝟎°)/𝟔𝟎 × 35 = 6° × 35 = 210° Hence, θ = 210° , r = 18 cm Now, Area swept by minutes hand = Area of sector = 𝜽/𝟑𝟔𝟎× 𝛑𝐫^𝟐 = 210/360×22/7× (18)2 = 7/12×22/7× 18 × 18 = 1/2×22/1 × 3 × 18 = 11 × 3 × 18 = 594 cm2
