The area of the sector formed by the 110 degree central angle is 50 units squared. What is the radius of this circle??

Question

mathstudent55 · Answer

You need the formula for the area of a sector of a circle.

anonymous · Answer

Solve the following for r:
$$\frac{110 \pi  r^2}{360}=50 $$$$r=30 \sqrt{\frac{2}{11 \pi }} $$

anonymous · Answer

Here's The Pic That Goes To My Question

anonymous · Answer

A complete cicle is 360 degrees and it's area is pi r^2.
110/360 pi r^2 is the area of 110 degrees of the same circle.

mathstudent55 · Answer

@gswag98 
This is a problem that needs a formula.
You need to either memorize the formula or know where to find it.
Then you need to know how to use it.

The formula for the area of  a sector of a circle is:

$A = \dfrac{\theta}{360^o}\pi r^2$

The Greek letter $\theta$ (called theta) represents the measure of the central angle that intercepts the arc. In your case, theta = 110 deg.
You know the area: A = 50.
You are looking for r.

The first step is to write the formula, which we have done above.
Now replace all the dimensions you were given (theta and A)

$50 = \dfrac{110^o}{360^o}(3.14159) r^2$

$50 = 0.95993r^2$

$\dfrac{50}{0.95993} = r^2$

$r^2 = 52.087$

Now take square root of both sides:

$r = 7.22$

anonymous · Answer

is that 7.22 rounded to two decimal plces

mathstudent55 · Answer

Yes.