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23 July, 18:01

A sector with an area of 140 pi cm2 has a radius of 20cm

What is the central angle measure of the sector in degrees?

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  1. 23 July, 19:41
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    Answer: The central angle measure is 126°

    Step-by-step explanation:

    The circle has a radius of 20cm

    The area of a sector of a circle of an angle A is:

    Area = (A/360°) * pi*r^2

    where r is the radius.

    Here we have that the area is (140*pi) cm^2

    let's find the value of A.

    (140*pi) cm^2 = (A/360) * pi * (20cm) ^2 = (A/360) * pi*400cm^2

    140 cm^2 = (A/360) * 400 cm^2

    A = (140/400) * 360° = 126°

    The central angle measure is 126°
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