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


Answer :


Clearly, minute hand of a clock describes a circle of radius equal to its length i.e., 14 cm. Since the minutes hand rotates through 6° in one minute, therefore, area swept by the minute hand in one minute is the area of sector of angle 6° in a circle of radius 14 cm. Hence, the required area i.e., the area swept in 5 minutes.

\(= \ ( \frac{ \theta}{360} \ × \ \pi r^2 \ × \ 5) \ \)
\( = \ \frac{6}{360} \ × \ \frac{22}{7} \ × \ (14)^2 \ × \ 5 \)
\(= \ \frac{1}{60} \ × \ \frac{22}{7} \ × \ 196 \ × \ 5 \ \)
\( = \ \frac{154}{3} \ cm^2 \)

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