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3 years ago

Need help badly #15 Find the area of each sector.

Mathematics

1 answer:

Ber [7]3 years ago

6 0

The highlighted sector is exactly 3/4 of the circle area, because $\frac{3\pi}{2}$ is 3/4 of $2\pi$ which is a complete rotation.

Since you are given the radius, you can compute the area as

$A = \pi r^2 = 16\pi$

So, 3/4 of this area would be $12\pi$ squared cm.

The remaining sector, of course, is $4\pi$ squared cm.

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Suppose a sector of a circle with radius r has a central angle of θ. Since a sector is a fraction of a full circle, the ratio of

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$\dfrac{A}{\pi r^2} =\dfrac{\theta}{2\pi}$

$A=\dfrac{\theta r^2}{2}, (\theta$ in radians)$

Step-by-step explanation:

Suppose a sector of a circle with radius r has a central angle of θ.

Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle of θ to the measure of a full rotation of the circle.

A full rotation of a circle is 2π radians.

This proportion can be written as: $\dfrac{A}{\pi r^2} =\dfrac{\theta}{2\pi}$

Multiply both sides by $\pi r^2$

$\dfrac{A}{\pi r^2} *\pi r^2=\dfrac{\theta}{2\pi}*\pi r^2$

Simplify to get:

$A=\dfrac{\theta r^2}{2}$

Where θ is the measure of the central angle of the sector and r is the radius of the circle.

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