The minute hand of a clock 6 inches long and moves from 12 to 7 o’clock. How far does the tip of the minute hand move?

Answer 1

A good formula to have memorized about a circle is:

ArcLength, L= rθ, where θ is the angle of the arc.

You should know this since the full circumference of a circle is: C=2πr, where θ=2π radians or 360°. (We have to use radians here)

For this case, θ=7/12C and r = 6 inches

L = (7/12)(2π)(6) = 7π ≈ 21.99114858 inches

Answer 2

If the tip of the minute hand is 6 inches from the center, it moves a total of 2πr = 2π(6) = 12π inches over the course of 12 hours. This represents one complete revolution of the tip of the minute hand

As it moves from 12 to 7, it moves a total of 7/12 of an entire revolution.

So, the tip of the minute hand moves (7/12)(12π) = 7π ≈ 21.99115 inches as it moves from 12 to 7