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12 February, 15:31

The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of pi and then round to 2 decimal places.

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  1. 12 February, 15:48
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    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
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