Question

The minute hand on a clock is 6 inches long. Between 1:15 p.m. and 1:40 p.m., the minute hand travels along an arc subtended by an angle of 150°. Approximately how many inches does the tip of the minute hand travel along the arc during that time?

Answer 1

To calculate the distance traveled along the arc, we can use the formula:

Distance = (Arc Length / Total Angle) * Circumference of the Circle

The circumference of the circle is given by 2πr, where r is the length of the minute hand (6 inches).

Total Angle = 360° (complete revolution)

Using the given values:

Total Angle = 360°

Arc Angle = 150°

Length of minute hand (r) = 6 inches

We can substitute these values into the formula to find the distance traveled along the arc:

Distance = (Arc Angle / Total Angle) * Circumference

Distance = (150° / 360°) * (2π * 6 inches)

Distance ≈ (5/12) * (2π * 6 inches)

Distance ≈ (5/12) * (12π inches)

Distance ≈ 5π inches

Therefore, the tip of the minute hand travels approximately 5π inches along the arc during the given time interval.