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Sum

The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am and 6:40 am.

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#### Solution

Length of the minute hand = 5 cm = Radius of the clock

Minutes between the time period 6:05 am to 6:40 am = 35 minutes

In 60 minutes, the minute hand completes one revolution, i.e. 360°.

∴ Angle made by minute hand in 1 minute = 360°/60° = 60°

Thus angle made by minute hand in 35 minutes = 60° × 35 = 210°

Angle made by minute hand in 35 minutes (in radians) = θ = `(210π)/180`

∴ Area swept by minute hand in 35 minutes = `1/2 r^2 theta`

= `1/2 xx 25 xx (210pi)/180`

= `1/2 xx 25 xx (210 xx 22)/(180 xx 7)`

= `275/6`

= 45.833 cm^{2}

Hence, the required area swept by the minute land is 45.833 cm^{2}

Concept: Area of Circle

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