Question

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

Answer 1

Answer:

154/3 $cm^{2}$

Step-by-step explanation:

1. minute hand completes 1 circle in one hour

• swept by minute hand in 1 hour [i.e, 60 mins]=360°
• swept by minute hand in 1 min [i.e, 60 sec]=360°/60°=6°

• swept by minute hand in 5 mins = 6°×5=30°

1. hence θ=30°,radius=14cm
2. the area swept by minutes hand = area of sector  

                                                              =θ/360° ×πr²  

                                                              =30°/360° × 22/7 × [14]²

                                                              =1/12 × 22/7 × 14 × 14

                                                              =1/12 × 22/1 × 2 × 14

                                                              =154/3 $cm^{2}$

• hence area swept by minute hand in 5 mins = 154/3 $cm^{2}$