Chapter 9.2, Problem 32E

To determine

To find: The diagram for the rotation completed by the hour hand of the clock during the time.

Answer to Problem 32E

The angle made by the hour hand is $1.33\pi$ or $240°$ and the diagram for it is shown in Figure 1 and the angle made by the hour hand is $17040°$ more than the hour hand.

Explanation of Solution

Given:

The work hours are 9:00 AM to 5:00 PM.

Calculation:

Consider the work hours are 9:00 AM to 5:00 PM.

Consider the total angle is of $360°$ .

Then each hour contribute to $\frac{360°}{12}$ that is $30°$ .

Then, the angle between 9 Am to 5 Pm is,

  $30°\left(8\right)=240°$

And is radians,

  $\begin{array}{c}240°=240°\left(\frac{\pi }{180°}\right)\\ =1.33\pi \end{array}$

The angle made by the hour hand between 9 AM to 5 PM is shown in Figure 1

  

Figure 1

Consider the angle made my minute hand in one hour is,

  $360°\left(60\right)=2160°$

Then, the angle covered by the minute hand between 9 AM to 5 PM is,

  $2160°\left(8\right)=17280°$

Thus, the angle covered by the minute hand is $17280°-240°=17040°$ more than the hour hand.