Determine the area of a circle with a 3 meter radius between 125 degrees and 212 degrees.

Question

I am unsure how to solve using the degrees.

Answer 1

I think this problem is asking you to find a section of the circle's area. You can think of the entire area of a circle as the area between 0° and 360°, since 360° is a full rotation. This problem wants you to find the area between 125° and 212°. That's a total of 212 - 125 = 87°, which is 87/360 = 29/120 of the circle's total area. We'll use this fact later.

 

First, let's find the circle's area.

 

A = πr²

A = π(3)²

A = 9π

 

The circle's total area is 9π m². But we're only looking for 29/120 of that. So, the area of the sector of the circle we're interested in is:

 

A_s = (9π)(29/120)

A_s = (261π)/120

As = (87π)/40

A_s ≈ 6.83

 

Therefore, the area of the circle between the given degrees is approximately 6.83 m².