What is the radius of a circle with a sector area of 7 pi sq. ft. and an arc whose measure is 70°?
6 feet
10 feet
18 feet

Question

What is the radius of a circle with a sector area of 7 pi sq. ft. and an arc whose measure is 70°?
6 feet
10 feet
18 feet

e.mccormick · Answer

Do you know the formula for arc area?

e.mccormick · Answer

If not, it is pretty easy to find it out as a simple percentage of the full circle area.

e.mccormick · Answer

As you probably know, the area of a cirle is $\pi r^2$.  Well, you can multiply anything by 1 and it is the same thing:

$\pi r^2 \cdot 1$  But what if I make my 1 look like this:

$\pi r^2 \cdot \dfrac{360}{360}$ 

Still the same thing.  BUT there is a new meaning.  For 360 degress out of a possible 360 degrees, the area is that.

Now, I can find any percentage by replacing the top 360 with the number involved:

$\pi r^2 \cdot \dfrac{70}{360}$ 

That is the formula for the area of your circle.  So set it equal to the area then solve for the radius.