Question

A clock has a minute hand that is 3 1/2 inches long. From 9:00 to 9:25 the hands on the clock move 150°. How many inches around the clock have the hands traveled?

Answer 1

To find the distance traveled by the clock hands, we need to find the arc length along the clock's circumference. This can be calculated using the fraction of the circumference covered by the angle between 9:00 and 9:25.

Step-by-step explanation:

To find the distance traveled by the clock hands in inches, we need to find the arc length along the clock's circumference. The angle covered by the hands from 9:00 to 9:25 is 150°.

Since the clock has 360° in a full revolution, we can find the fraction of the circumference covered by the hands in this time period:

fraction = (angle covered) / (360°)

The circumference of the clock can be found using the formula:

circumference = 2π(radius)

Substituting the given radius, we can find the arc length traveled by the hands as:

arc length = (fraction) * (circumference)