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

Step 1: Understanding the Concept:
The hour hand of a clock completes one full rotation (\(360^\circ\)) in 12 hours (720 minutes). We need to calculate the time elapsed and the corresponding angle.
Step 2: Key Formula or Approach:
1. Rate of hour hand = \( \frac{360^\circ}{12 \text{ hours}} = 30^\circ/\text{hour} \). 2. Rate of hour hand = \( \frac{30^\circ}{60 \text{ min}} = 0.5^\circ/\text{minute} \).
Step 3: Detailed Explanation:
1. Calculate total time elapsed: From 7:00 a.m. to 8:10 a.m. = 1 hour and 10 minutes. Total minutes = \( 60 + 10 = 70 \) minutes. 2. Calculate the angle: \[ \text{Angle} = 70 \text{ minutes} \times 0.5^\circ/\text{minute} \] \[ \text{Angle} = 35^\circ \]
Step 4: Final Answer:
The angle swept by the hour hand is 35°.