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) = [tex]2\pi r[/tex] {where r is radius of circle}
= [tex]2 \times \pi \times 8[/tex] {given r = 8 inches long}
= [tex]16 \pi[/tex]
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 [tex]\frac{25}{60}[/tex] which is [tex]\frac{5 }{12}[/tex] of the circumference, that means;
The length of arc from time 12:00 to 12:25 = [tex]\frac{5}{12}\times \text {Circumference of circle}[/tex]
= [tex]\frac{5}{12} \times 16 \pi[/tex]
= [tex]\frac{20}{3} \pi[/tex] = 6.67[tex]\pi[/tex]
Now, assuming value of [tex]\pi[/tex] = 3.14; so 6.67[tex]\pi[/tex] = [tex]6.67 \times 3.14[/tex] = 20.9 inches (in nearest tenth)
Hence, the tip of the minute hand travels 20.9 inches.
