Question

The length of minute hand of the clock is 14 cm. Find the area swept by minute hand from 9:00 to 9:30.

Answer 1

It is given that the length of minute hand is cm.
So, we can say that the radius is 14cm.

According to the question , we have to find the area swept by minute hand during 9:00 to 9:30
During this time, the time consumed will be 9:00- 9:30= 30 minutes.

In a minute, the hand of clock rotates by 6°. So,
In 30minutes = the hand will rotate by
30 X 6 = 180



Also, It can be observed that it forms a sector while rotating.
So, using sector formula.
So, θ = 180

Hence, the area swept by minute hand is
=( theta/360)×pi (radius)^2
=(180/360)×pi×(14)^2
=pi (14)^2/2
=3.14×(14)^2/2
=3.14×196/2
=615.44/2
=307.72cm^2