Question

a clock shows the time: what time will it be when the the hour hand has rotated 180°? the time will be \\(\square\\) oclock, \\(\square\\) hours later. calculator

Explanation:

Step1: Determine the angle per hour mark

A clock is a circle, which is \(360^\circ\). There are 12 hour marks, so the angle between each hour mark is \(\frac{360^\circ}{12} = 30^\circ\) per hour mark.

Step2: Calculate the number of hours for \(180^\circ\) rotation

To find how many hours correspond to a \(180^\circ\) rotation, we divide \(180^\circ\) by the angle per hour mark (\(30^\circ\)): \(\frac{180^\circ}{30^\circ}=6\) hours.

Step3: Find the current time and the new time

The current time shown on the clock is 5 o'clock (since the hour hand is on 5 and the minute hand is on 12). Adding 6 hours to 5 o'clock: \(5 + 6 = 11\) o'clock.

Answer:

The time will be \(\boldsymbol{11}\) o'clock, \(\boldsymbol{6}\) hours later.