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21 January, 13:56

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

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  1. 21 January, 17:00
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    Answer: the angle measure of the arc bounding a sector is 45.86 degrees

    Step-by-step explanation:

    The formula for determining the area of a sector is expressed as

    Area of sector = θ/360 * πr²

    Where

    θ represents the central angle.

    r represents the radius of the circle.

    π is a constant whose value is 3.14

    From the information given,

    Diameter = 10 miles

    Radius = diameter/2 = 10/2 = 5 miles

    Area of sector = 10 square miles

    Therefore,

    10 = θ/360 * 3.14 * 5²

    10 = θ/360 * 78.5

    78.5θ = 10 * 360 = 3600

    θ = 3600/78.5

    θ = 45.86 degrees
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