Find area of sector of circle

Question

Please help!

find the are of a 25degree sector of a circle which has a diameter of 12 inches

Answer 1

A=∏r^2

diameter=12 inches, radius=6 inches

A=∏6^2

A=36∏ is the area of the circle

you want 25/360 of the area of the circle

25/360=5/72

area of the sector=(5/72)(36∏)

area of the sector =5∏/2, or 2.5∏ or...

area of the sector=2.5*3.14159

area of the sector=7.853975 square inches (round as needed)

Answer 2

There is a formula for this, but it is easier to think it through logically. A sector is a fraction of the entire circle's area. What fraction? If the central angle is 25, then the fraction is 25/360.

The area of the circle is given by A = πr². In this case A = 36π.(radius is 6 if diameter is 12)

So the area of the sector is 25/360 (36π) .

You should be able to cancel and reduce before multiplying. (25/10)π or 5π/2 square inches.

That is an exact answer. Approximate by using an approximation for π if asked to do so.

Answer 3

Hi Clara,

You'll want to start by determining the circumference of the circle itself. We know that the diameter is 12, and since radius = d/2, then the radius is 6. Now we can plug the radius value into the formula for circumference of a circle, 2(pi)(r), and we get 2(pi)6 = 37.7 as the circumference of the circle.

Now for the sector. The arc of a sector of a central angle is equivalent to the degrees of the angle needed to make the arc. Since there are 360 degrees in the whole circle, and we only want the measure of 25 degrees, we will divide 25 by 360. 25/360= .069. This is the portion of the circumference we're looking for.

So take the 37.7 circumference of the whole circle and multiply it by the .069 portion that represents 25 degrees, and we get 2.618.

Hope this helps!

Have a great night and be safe.

michael.russell.10