Question

A circles has radius 10 centimeters. Suppose an arc on the circle has length 8\pi centimeters. what is the measure of the central angle whose radii define the arc?

Answers

  1. Answer:

    The measure of the central angle whose radii define the arc is \mathbf{\frac{4\pi }{5} }

    Step-by-step explanation:

    Radius of circle = 10 cm

    Length of arc = 8\pi

    We need to find Theta \theta

    The formula used will be: S=r \theta

    S= length of arc, r = radius and \theta = angle

    Putting values and finding \theta

    S=r \theta\\8\pi =10 \theta\\\theta=\frac{8\pi }{10} \\\theta=\frac{4\pi }{5}

    So, the measure of the central angle whose radii define the arc is \mathbf{\frac{4\pi }{5} }

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