Question

The minute hand of a clock is 12cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

Answer 1

Given: Length of minute hand = 12cm

Let us look at a clock:

So, minute hand covers a total of 60 minutes in one round of the clock.

So, 60 minutes = 360˚

1 minute = 360˚/60˚ = 6˚

35 minutes = (35 × 6)˚ = 210˚

So in 35 minutes, minute hand subtends an angle of 210˚.

Now Area of segment  = θ/360˚ πr²

Where θ is the angle subtended.

Therefore, the area covered by minute hand = 210˚/360˚ πr²

The radius of the circle = Length of the minute hand = 12cm

The area covered by minute hand  = 7/12 x 22/7 x 12²

The area covered by minute hand = (22 × 12) cm²

Area = 264 cm²

Hence, The area covered by minute hand in 35 minutes is 264cm².