Question

Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? Part 2: How far does the tip of the minute hand travel during that time?

Answer 1

Part 1:

From 1:20 to 1:55 is a total of 35 minutes. Since the minute hand completes one full rotation in 60 minutes, it moves halfway around the clock during this time. Therefore, the minute hand moves pi (or 180 degrees) radians.

Answer: pi (or 180 degrees)Part 2:

Since the minute hand has a length of 6 inches, we can use the formula for the circumference of a circle to find how far the tip of the minute hand travels during this time.

C = 2pir

C = 2pi6

C = 12pi

So the tip of the minute hand travels a total distance of 12pi inches during the 35 minutes from 1:20 to 1:55.

Answer: 12*pi inches