Question

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.

Answer 1

The first option.

Reason: A sector is a fraction of the whole circle equal to its central angle divided by 360°. So (angle/360) × (area of circle = πr²) gives the sector’s area.