In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula StartFraction measure of angle Z Y X Over 360 degrees EndFraction (pi r squared).

Circle Y is shown. Line segments X Y and Z Y are radii. Sector X Y Z is shaded.

Which best explains the formula?
The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
The central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.
The central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.
The central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

The best explanation for the formula is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

What is the Area of a sector of a Circle?

The area of a sector of a circle equals measure of the central angle subtended by the sector over the angle measure of a full circle multiplied by the area of the circle.

A full circle has an angle measure of 360 degrees.

The area of a circle = pi(r²).

Therefore, the formula for the shaded sector of a circle would be represented by the formula: ∅/360 × πr².

Here, we have:

Central angle (∅) = measure of angle ZYX

Measure of full circle = 360 degrees

Area of a circle = πr². (area formula for the circle that contains the sector)

Therefore, the statement that best explains the formula, (m∠ZYX)/360 × πr², used for finding the shaded sector in the circle is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

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