What is the area swept by the minute hand in 14 minutes

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Solution

Q.
A pendulum clock uses a swinging weight as its timekeeping element. Invented in 1656 by Christiaan Huygens, the pendulum clock was the most precise timekeeper in the world, which is why it became so widely used. Its accuracy helped support the faster pace of life necessary for the Industrial Revolution. By the 1930s and 40s, home pendulum clocks were largely replaced by more affordable synchronous electric clocks. Today, pendulum clocks are mostly valued for their decorative and antique qualities.

Dhaani bought a pendulum clock for her living room. The clock features a small pendulum with a length of 45 cm. The minute hand is 14 cm long, while the hour hand is 6 cm long.

Based on the above information, answer the following questions

(i) What is the area swept by the minute hand in 14 minutes

1 $143.73 c m^{2}$

2 $143.72 c m^{2}$

3 $140.73 c m^{2}$

4 $139.73 c m^{2}$

Ans.
(1)

Angle described by a minute hand in 14 minutes $= 6 ° \times 14 = 84 °$

$R a d i u s r = 14 c m (l e n g t h o f m i n u t e h a n d) ∴ Area swept by the minute hand = \frac{84 °}{360 °} \times \frac{22}{7} \times (14)^{2} = \frac{2156}{15} \approx 143.73 c m^{2}$

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