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3 years ago

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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 ro

und any intermediate computations. round your answer to the nearest tenth.

1 answer:

ArbitrLikvidat [17]3 years ago

6 0

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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