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

The tip of the minute hand travels 20.9 inches.

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 * \pi * 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
`(25)/(60)` which is
`(5 )/(12)` of the circumference, that means;

The length of arc from time 12:00 to 12:25 =
`(5)/(12)* \text {Circumference of circle}`

=
`(5)/(12) * 16 \pi`

=
`(20)/(3) \pi` = 6.67
`\pi`

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

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