Answer: 12.56 inches
Step-by-step explanation: First, when know the following:
A clock is a circle, so the total movement, from 12 to 12 is 360° or 2π.
It is also know that a circle circunference (The total size of the circle on a straight line) is 2π * Radius
The minute hand does a circle on its travel, that circle radius is equal to 6 inches.
The movement from 12 to 4 is a third (4/12 = 1/3). Knowing this:
120° = (1/3) * 360° = (1/3) * 2π = (2/3) * π
So the travel from 12 to 4 is (2/3)π
To know the distance on inches, we multiply the distance on radians per the radius.
Total distance = 6 * (2/3)π
Total distance = 4π inches
Total distance = 12.56 inches