Question

The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

• A. \(\frac{35}{4}^\circ\)
• B. \(\frac{35}{2}^\circ\)
• C. 35°
• D. 70°

Hint:

The length of the hand (7 cm) is extra information here as the question asks for the \textit{angle}, not the \textit{area} or \textit{distance}.

Answer 1

The Correct Option is C

To find the angle swept by the hour hand between 7:00 a.m. and 8:10 a.m., we can use the fact that the hour hand of a clock completes a full circle, which is 360°, in 12 hours.

First, calculate the angle swept by the hour hand in one hour. The formula is:

1. \(Angle = \frac{360^\circ}{12} = 30^\circ\)

Next, determine how many minutes past 7:00 it is when the time is 8:10 a.m.:

1. \(8:10 \text{ a.m.} - 7:00 \text{ a.m.} = 1 \text{ hour and } 10 \text{ minutes}\)

Convert 10 minutes into a fraction of an hour. Since there are 60 minutes in an hour:

1. \(10 \text{ minutes} = \frac{10}{60} = \frac{1}{6} \text{ of an hour}\)

The total time elapsed from 7:00 a.m. to 8:10 a.m. is:

1. \(1 + \frac{1}{6} = \frac{7}{6} \text{ hours}\)

Finally, calculate the angle swept by the hour hand in \(\frac{7}{6}\) hours:

1. \(Angle = \frac{7}{6} \times 30^\circ = 35^\circ\)

Thus, the angle swept by the hour hand between 7:00 a.m. and 8:10 a.m. is 35°. The correct answer is \(35^\circ\).