A sector of a circle with a 120 degree arc has an area of 75(pi)in^2. Find the radius.

Question

A sector of a circle with a 120 degree arc has an area of  75(pi)in^2. Find the radius.

anonymous · Answer

Basically, you must first find out the formula for the sector of a circle. From there on, you can find the radius. The formula of a sector is: 

$$\theta*r ^{2}$$

The reason as to why this is the formula is simple: because a sector is actually a fraction of the full circle.

Now you can easily find the radius of that circle, if you set up an equation:

$$\theta r^{2} = area$$
and solve for r

anonymous · Answer

Maybe I didn't explain the reason as to why that is the formula properly. As I was saying, a sector is just a part of the circle. What part? well, it's $$\frac{\theta}{2 \pi}$$ parts of the circle. So you do 
$$\frac{\theta}{2 \pi} * \pi r ^{2} = \frac{\theta r ^{2}}{2}$$

Thus, it looks like formula I gave you in the first post was wrong.

anonymous · Answer

you can see that  120/360 is a third.....

anonymous · Answer

my intention was to give a general approach for solving similar problems