Question 24 (Choice 1) The length of the minute hand of a clock is 6 cm. Find the area swept by it when it moves from 7:05 p.m. to 7:40 p.m.
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 = 3210° , r = 6 cm
Now,
Area swept by minutes hand = Area of sector
= θ/360×πr2
= 210/360×22/7×(14)2
= 1/2×22/1 × 6
= 11 × 6
= 66 cm2
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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