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18 August, 11:41

The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?

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  1. 18 August, 12:09
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    A = (απr^2) / 360 = (απd^2) / 1440 (r^2=d^2/4)

    α=1440A / (πd^2)

    s=απd/360 (where s=arc length) so

    s = (1440Aπd) / (360πd^2)

    s=4A/d and since A=10mi^2 and d=20mi

    s = (4*10) / 20

    s=2 miles
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