Question : The minute hand of a clock is 20 cm long. Find the area on the face of the clock swept by the minute hand between 8 a.m. and 8:45 a.m.
Option 1: $\frac{6600}{7}$ cm2
Option 2: $\frac{6600}{9}$ cm2
Option 3: $\frac{6600}{18}$ cm2
Option 4: $\frac{6600}{14}$ cm2
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Correct Answer: $\frac{6600}{7}$ cm 2
Solution :
Length of minute hand = 20 cm
As we know the 1 minute angle made by the minute hand is $6^\circ$
In 45 minutes, the minute hand will make = $45(6^\circ)= 270^\circ$
Area swept by minute hand in 45 minutes
= $\frac{\theta}{360^{\circ}}\times \pi r^2$
= $\pi\times 20^2\times \frac{270}{360}$
=$\frac{6600}{7}$ cm
2
Hence, the correct answer is $\frac{6600}{7}$ cm
2
.
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