✪ Question :- the minute of the hand clock is 5cm long.Find the area describe by the minute on the face of the clock betweem 7:00Am to 7:22Am. ?✰ Concept and formula used :-
➳ Minute hand of a clock Make an angle of 6° in one minute .
➳ Area of sector of circle is given by : - (Angle at centre/360°) * πr² .❁ Solution :-
it is given that, Minute hand travel from 7:00 AM to 7:22 AM .
→ it travel = 7:22 - 7:00 = For 22 minutes .
→ Angle he made = 22 * 6 = 132° .
Now, Area of sector he made ,
⟿ Area = (132/360) * π * (5)²
⟿ Area = 0.367 * 3.14 * 25
⟿ Area = 28.80cm² . (Aprrox)Hence, the minutes hand describe the area of 28.80cm² in given time..❦❦ Extraknowledge ❦❦:-
☛ The dial of the clock is circular in shape and was divided into 60 equal minute spaces..
☛ 60-minute spaces trace an angle of 3600. Therefore, 1minute space traverses an angle of 60..
☛ In 1 hour, Minute hand traverses 60-minute space or 3600 , Hour hand traverses 5-minute space or 300..
☛ The hands of the clock are perpendicular in 15-minute spaces apart
☛ The hands of the clock are in straight line and opposite to each other in 30-minute spaces apart.
☛ The hands of the clock are in straight line when they coincide or opposite to each other.
☛ The hands of the clock are perpendicular to each other for 22 times in 12 hours and for 44 times in a day.
☛ The hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.
☛ The minute hand gain 55 minutes over hour hand per hour.
The minute of the hand clock is 5cm long.Find the area swept by the minutes hand on the face of the clock betweem 7:00Am to 7:22ASolution :The length of the minute's hand is 5 cm To finDArea swept by the minute's hand between 7:00 and 7:22We would need to find the angle between 7:00 and 7:22 The minute hand sweeps 360° in 60 minutes Implies,it would cover 6° in one minute
In 22 minutes,∅ = 22 × 6 = 132°
The minute's hand forms an arc between 7:00 and 7:22
Substituting the values,we write :The area swept by the minute's hand between 7:00 and 7:22 is 28.78 cm²
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anyway have a nice evening : )
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