Bunuel wrote:
Which of the following is closest to the distance traveled by the tip of a 9-inch hour hand of a clock in 18 minutes?
A. 17 inches
B. 10.8 inches
C. 5.4 inches
D. 3 inches
E. 1.4 inches
In 12 minutes, the hour hand moves by \(\frac{30}{5} = 6\) degree. The hour hand moves 9 degree in 18 minutes.
We can now represent this as a sector with an angle of 9 degrees and the radius of the circle is 9 inch.
Diagrammatic representation
Attachment:
Distance_Clock.png [ 4.63 KiB | Viewed 398 times ]
Formula used: Length of the sector = \(\frac{A}{360} * 2 * \pi * R\) where A = angle of sector
Length = \(\frac{A}{360} * 2 * \pi * R = \frac{9}{360} * 2 * \pi * 9 = \frac{1}{20} * \frac{22}{7} * 9 = \frac{11*9}{10*7} = \frac{99}{70} = 1.4\) inches
Therefore, the distance travelled by the hour hand is the length of the sector, which is
1.4 inches(Option E)
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