What is the area swept by the minute hand in 5 minute if the length of the minute hand of a clock is 40 cm?

The length of 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.

Minute hand of the clock describes a circle of radius equal to its length i.e 5 cm.
The minute hand rotates through 6o in one minute.
So, the minute hand will sweep 210o in one minute.
Area swept by the minute hand in one minute is the area of a sector of angle 6o in a circle of radius 5 cm.
Area swept by the minute hand in 35 minutes is the area of a sector of angle 210o in a circle of radius 5 cm

Area of sector=`θ/360xxpir^2`

`=210/360xxpixx(5)^2`

`=45 5/6 cm^2`

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Page 2

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Angle make by the minute hand in 1 minute = 6∘
Angle make by the minute hand in 5 minute = 5 ⨯ 6∘ = 30∘
Area of the sector having central angle is given by

`(30°)/(360°) pi(14)^2`

`=1/12 xx22/7(14)^2`

`=51.33 cm^2`

Hence, the area swept by minute hand in 5 minutes is 51.33 cm2

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Solution:

We use the formula for the area of the circle to find the area swept by the minute hand.

We know that the minute hand completes one rotation in 1 hour or 60 minutes.

Therefore, area swept by the minute hand in 60 minutes = Area of the circle with radius equal to the length of the minute hand = πr2

Using unitary method, we get