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

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

Solution:

Length of minute hand = radius of the clock (circle)

∴ Radius (r) of the circle = 14 cm (given)

Angle swept by minute hand in 60 minutes = 360°

So, the angle swept by the minute hand in 5 minutes = 360° × 5/60 = 30°

We know,

Area of a sector = (θ/360°) × πr²

Now, area of the sector making an angle of 30° = (30°/360°) × πr² cm²

= (1/12) × π14²

= (49/3)×(22/7) cm²

= 154/3 cm²