Question : The hour hand moves through 4 hours and has a length of 6 cm. Find the area (in cm2, rounded off to two decimal places) of the sector covered by the hour hand.
Option 1: 32.69
Option 2: 30.67
Option 3: 37.71
Option 4: 35.75
Correct Answer: 37.71
Solution :
In 4 hours, the hour hand covers = $0.5° \times 4 \times 60 = 120°$
Now, the area of the sector covered by the hour hand = $\pi \times 6^2\times \frac{120°}{360°}$
⇒ Area = $12\pi = 37.71\ \mathrm{cm^2}$
Hence, the correct answer is 37.71.
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