Question

Determine the area of the green sector.

Answer 1

The area of the green sector is 22.33646, you can shorten that down to 22.34 if you would like. But this is the correct answer. :)

(My Work: Area of a Circle= pi(r)^2 so I took your radius provided and plugged it in. pi(3)^2=28.274... and since you have 75 degrees cut out, I multiplied by .21 since 75/360=.21. I took that answer and subtracted it from our original (28.274) to get the final answer: 22.34)

Hope this helped and wasn't to confusing!

Answer 2

Since the radius of this circle is 3 inches, the area of the green sector is 57π/8 square inches.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = π
`r^2` × θ/360

Where:

• r represents the radius of a circle.
• θ represents the central angle.

Note: The measure of an intercepted arc is equal to the central angle of a circle.

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = π
`r^2` × θ/360

Area of sector = π ×
`3^2` × 285/360

Area of sector = π × 9 × 57/72

Area of sector = π × 57/8

Area of sector = 57π/8 square inches.