This question is similar to CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard

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https://www.teachoo.com/19024/4114/Question-24-Choice-1/category/CBSE-Class-10-Sample-Paper-for-2023-Boards---Maths-Standard/

 

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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 cos⁡θ+sin⁡θ=1 Squaring both sides (cos⁡θ+sin⁡θ )^2=1^2 〖𝒄𝒐𝒔〗^𝟐⁡𝜽+〖𝒔𝒊𝒏〗^𝟐⁡𝜽+2 𝑐𝑜𝑠⁡𝜃 𝑠𝑖𝑛⁡𝜃=1 Putting 〖𝑐𝑜𝑠〗^2⁡𝜃+〖𝑠𝑖𝑛〗^2⁡𝜃 = 1 𝟏+2 𝑐𝑜𝑠⁡𝜃 𝑠𝑖𝑛⁡𝜃=1 2 𝑐𝑜𝑠⁡𝜃 𝑠𝑖𝑛⁡𝜃=1−1 2 𝑐𝑜𝑠⁡𝜃 𝑠𝑖𝑛⁡𝜃=0 𝒄𝒐𝒔⁡𝜽 𝒔𝒊𝒏⁡𝜽=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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.