Facts About Clocks :-
(i) Angle described by minute hand in 60 minutes = 360ᵒ
360
(ii) Angle described by minute hand in 5 minutes = (------- X 5) = 30ᵒ
60
(iii) Angle described by hour hand in 12 hours = 360ᵒ
Angle described by hour hand in 1 hour = 30ᵒ
Example.) The minute hand of a clock is 12 cm long. Find the area swept by it in 20 minutes
Ans.) Angle described by minute hand in 60 minutes = 360⁰
360
Angle described by minutes hand in 15 minutes = (------ X 20)⁰ = 120⁰
60
Thus, required area is the area of a sector of a circle with central angle, θ = 120⁰ and radius, r = 12 cm
πr²θ
So, required area = (--------)
360
22 120
= (------ X 12 X 12 X -------) cm²
7 360
22 X 4 X 12
= (--------------) cm² = 150.85 cm² (Ans.)
7