The hour hand of a clock is 6cm long . Find the area swept by it between 11:20 am and 11:55am ?
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76
Solution:
Length of the hour hand of the clock = 6 cm
∴Radius of the sector described by the hour hand ( r ) = 6 cm
Given time = 11:20 am to 11:55 am
i.e. 55 - 20 min = 35 min = 35/60 h
In 1 hour , the hour hand rotates 30°.
Thus, Central angle of the sector :
= 30 × 35/60
= 35/2
= 17.5°
∴Area of the sector swept by the hour hand:
= 17.5/360 × 22/7 × 6 × 6 cm²
= 2.5 × 22/10 cm²
= 5.5 cm²
Hence, The required area swept by the hour hand is 5.5 cm².
Length of the hour hand of the clock = 6 cm
∴Radius of the sector described by the hour hand ( r ) = 6 cm
Given time = 11:20 am to 11:55 am
i.e. 55 - 20 min = 35 min = 35/60 h
In 1 hour , the hour hand rotates 30°.
Thus, Central angle of the sector :
= 30 × 35/60
= 35/2
= 17.5°
∴Area of the sector swept by the hour hand:
= 17.5/360 × 22/7 × 6 × 6 cm²
= 2.5 × 22/10 cm²
= 5.5 cm²
Hence, The required area swept by the hour hand is 5.5 cm².
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12
Correct answer :-
5.5cm^2
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