Question

The minute hand of a clock is 8 inches long. To the nearest tenth of an inch, how far does the tip of the minute hand travel as the time progresses from 12:00 to 12:25.
The tip of the minute hand travels ________ inches

Answer 1

Answer:

The tip of the minute hand travels 20.9 inches.

Step-by-step explanation:

We are given that the minute hand of a clock is 8 inches long. And we have to find that how far does the tip of the minute hand travel as the time progresses from 12:00 to 12:25.

So, firstly we will find the circumference of circle;

       Circumference of circle (C)  =  $2\pi r$   {where r is radius of circle}

                                                      =  $2 \times \pi \times 8$   {given r = 8 inches long}

                                                      =  $16 \pi$

Now, as we know that the minute hands completes the full circle in 60 minutes, therefore, the length of the arc between time 12:00 to 12:25 represents  $\frac{25}{60}$  which is  $\frac{5 }{12}$  of the circumference, that means;

The length of arc from time 12:00 to 12:25  =  $\frac{5}{12}\times \text {Circumference of circle}$

                                                                       =  $\frac{5}{12} \times 16 \pi$

                                                                       =  $\frac{20}{3} \pi$ = 6.67$\pi$

Now, assuming value of $\pi$ = 3.14; so 6.67$\pi$ =  $6.67 \times 3.14$ = 20.9 inches (in nearest tenth)

Hence, the tip of the minute hand travels 20.9 inches.