Question

The minute hand of a clock is 8 inches long and moves from 12 to 9 ​o'clock. How far does the tip of the minute hand​ move? Express your answer in terms of pi and then round to two decimal places.

Answer 1

Answer:
`12\pi` inches

Explanation:

Given : The minute hand of a clock is 8 inches long and moves from 12 to 9 ​o'clock.

From the attached image below ,

The angle made by minute hand from 12 to 9 ​o'clock (central angle)
`=(9)/(12)*360^(\circ)=270^(\circ)`

The length of the tip = radius (r)= 8 inches

The distance traveled by the tip of the minute hand​ = Arc formed from 12 to 9 ​o'clock.

Formula to find arc length =
`\frac{\text{Central angle}}{360^(\circ)}*2\pi r`

`=(270^(\circ))/(360^(\circ))*2\pi (8)\\\\=12\pi`

Hence, the distance traveled by tip of the minute hand​=
`12\pi` inches