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5 October, 08:27

A circle has a radius of 6 m. a sector of the circle has a central angle of 3?4 radians. find the area of the sector. do not round any intermediate computations. round your answer to the nearest tenth.

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  1. 5 October, 08:34
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    A circle has a general formula for area as:

    A = (θ / 360°) * π * r^2

    So when we are to look for the area of the circle, the θ = 360° and the factor (θ / 360°) is simply equals to 1 and is removed from the formula. However in this case, we are to find for the area of a portion of a circle, specifically a sector.

    It is given that the radius is 6 m and the central angle intercepted by this sector is 3 / 4 radians. As we can see in the formula, the angle θ is expressed in degrees, therefore we need to convert the central angle first into degrees.

    Central angle θ = (3 / 4 rad) (180° / π rad)

    Central angle θ = (135/π) °

    So the area of the sector is:

    A sector = (135/π / 360) * π * (6 m) ^2

    A sector = 13.5 m^2
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