Question

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 BLANK 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 Aπr2=BLANK. Multiply both sides by πr2 and simplify to get BLANK, where θ is the measure of the central angle of the sector and r is the radius of the circle.

Answer 1

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 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 A/πr^2 =θ2π. Multiply both sides by πr2 and simplify to get A= θ/2 r^2 , where θ is the measure of the central angle of the sector and r is the radius of the circle.

Explanation:

i hope this helps a bit

Answer 2

Central angle of θ

`(A)/(\pi r^2) =(\theta)/(2\pi)`

`A=(\theta r^2)/(2), (\theta$ in radians)`

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:
`(A)/(\pi r^2) =(\theta)/(2\pi)`

Multiply both sides by
`\pi r^2`

`(A)/(\pi r^2) *\pi r^2=(\theta)/(2\pi)*\pi r^2`

Simplify to get:

`A=(\theta r^2)/(2)`

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