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13 December, 08:43

The radius of a quarter circle is 4 kilometers. What is the quarter circle's perimeter?

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  1. 13 December, 08:50
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    14.283 km

    Step-by-step explanation:

    The circumference of the entire circle is given by ...

    C = 2πr

    so the length of the curved perimeter of the quarter-circle is 1/4 of that:

    1/4C = (1/4) 2πr = (π/2) r

    The straight sides of the quarter-circle are both equal to the radius, so the total of all sides of the quarter-circle is ...

    P = 2r + (π/2) r = (2+π/2) r

    P ≈ (3.570796) (4 km) ≈ 14.283 km

    The quarter-circle's perimeter is about 14.283 km.
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