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. $\left(\frac{35}{4}\right)^\circ$
• B. $\left(\frac{35}{2}\right)^\circ$
• C. $35^\circ$
• D. $70^\circ$

Hint:

Remember these standard rates for clock hands:
- The minute hand rotates at a rate of $6^\circ$ per minute.
- The hour hand rotates at a rate of $0.5^\circ$ per minute.
Keep these constants memorized to quickly solve any clock-related questions.

Answer 1

The Correct Option is C

Step 1: Split the time interval into a whole hour and extra minutes.
Instead of converting the entire 7:00 a.m. to 8:10 a.m. gap into minutes and multiplying once, let us handle the full hour and the leftover minutes as two separate pieces and add their angles.

Step 2: Angle swept during the full hour, from 7:00 a.m. to 8:00 a.m.
The hour hand completes a full $360^{\circ}$ turn in 12 hours, so in one hour it sweeps
\[ \frac{360^{\circ}}{12} = 30^{\circ} \]
Step 3: Angle swept during the extra 10 minutes, from 8:00 a.m. to 8:10 a.m.
In 60 minutes the hour hand sweeps $30^{\circ}$, so in 10 minutes, which is $\frac{10}{60} = \frac{1}{6}$ of an hour, it sweeps
\[ \frac{1}{6} \times 30^{\circ} = 5^{\circ} \]
Step 4: Add the two parts together.
\[ \text{Total angle} = 30^{\circ} + 5^{\circ} = 35^{\circ} \] The length of the hour hand, $7\text{ cm}$, is extra information here; it affects how far the tip travels but not the angle swept.

Final Answer:
The angle swept by the hour hand is $35^{\circ}$, which corresponds to option (C). \[ \boxed{35^{\circ}} \]