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

Step-by-step 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)$=\dfrac{9}{12}\times360^{\circ}=270^{\circ}$

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 = $\dfrac{\text{Central angle}}{360^{\circ}}\times2\pi r$

$=\dfrac{270^{\circ}}{360^{\circ}}\times2\pi (8)\\\\=12\pi$

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