THE LENGTH OF THE MINUTE HAND OF A CLOCK IS 6.3CM . FIND THE AREA SWEPT BY THE MINUTE HAND DURING THE TIME PERIOD 5:45AM TO 6:10 AM AD ALSO FIND THE DISTANCE DISTANCE TRAVELLED BY THE MINUTE HAND DURING THIS PERIOD.

We know that in 1 hour (i.e., 60 minutes), the minute hand rotates 360°.

In 25 minutes, minute hand will rotate = (3600/ 600) × 25 = 1500

Therefore, the area swept by the minute hand in 25 minutes will be the area of a sector of 150° in a circle of 6.3 cm radius.

Area of sector of angle θ =( θ/3600) × πr2

Area of sector of 150° = (1500/3600) × (22/7) × 6.3 ×6.3 = (10395/200) = 51.975 cm2

Therefore, the area swept by the minute hand in 25 minutes is 51.975 cm2

Distance travelled by minute hand to cover 25 minutes is the length of the arc AB:

Therefore,

Length of the arc AB = ( θ/3600) × 2πr = (1500/3600) × 2× (22/7) × 6.3 = (33/2) cm.

 

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