Question

The minute hand of a clock is 4 inches long. how far does the tipof the minute hand move in 20 minnutes?

Answer 1

The tip of the minute hand moves approximately (8/3)π inches in 20 minutes, using the circumference of the circular path it follows and the proportion of the path covered in that time.

Step-by-step explanation:

The student is asking about the distance traveled by the tip of the minute hand of a clock over a 20-minute period. To find the distance, we'll consider the movement of the minute hand as part of a circular path, which is described by the arc length of the circle segment.

The length of the minute hand, which is 4 inches, acts as the radius (r) of the circle. The minute hand completes one full rotation around the clock face in 60 minutes, so in 20 minutes, it covers one-third of a full rotation. We can find the arc length of the minute hand's path using the formula for the circumference of a circle (C = 2πr), multiplied by the fraction of the rotation:

Circumference: C = 2π(4 inches) = 8π inches

Arc Length for 20 minutes: (1/3) × 8π inches = (8/3)π inches

Therefore, the tip of the minute hand moves approximately (8/3)π inches in 20 minutes.

Answer 2

This is an arc length question, but it's a little hidden. The minute hand is the radius of the circle, so r=4. Next we need to know how much of the circle the tip of the minute hand will move through. Since there are 60 minutes in an hour, the minute hand will pass through 20/60=1/3 of the clock. Then we just use the circumference formula scaled by the amount of the clock we have:

`l=2\pi(4)((1)/(3))`