Question

A minute hand of a clock is 16 in long. Find the distance traveled by the tip of the minute hand in one hour

Answer 1

so the minute hand in 1 hour will cover the entire circular clock, so the 16 in long minute hand will do a full 360°.

`\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=16\\ \theta =360 \end{cases}\implies s=\cfrac{(360)(\pi )(16)}{180}\\\\\\ s=32\pi \implies s\approx 100.53`

Answer 2

The length of a clock hand is the length of the radius of a circle.

The minute hand needs to travel a full circle in one hour.

This length of travel would be the circumference of the circle.

To find the circumference of a circle multiply the radius by 2 and then multiply by PI (π).

Circumference = 16 x 2 x PI

Circumference = 32 x PI

Using 3.14 for PI:

Circumference = 32 x 3.14 = 100.48 inches. Round answer as needed.