Answer:
Step-by-step explanation:
To find the area of a circle, the formula you will be using is:
> A = pi * r^2
The first step to solving this is to find the full area of the circle. To find this, we must find how much of the given area is compared to the entirety of the circle. You can do this by dividing the given angle (170°) by the full angle of a circle (360°).
> 170 / 360 = 17/36 of the circle's area is NOT given
> 36/36 = 19/36 of the circle's area is given
Now, we know that 19/36 of the circle's area is equal to 59.698. We will find the full area through a bit of algebra.
> fullArea * partialAreaFraction = partialArea
> A * (19/36) = 59.598
> (A * (19/36)) / (19/36) = 59.598 / (19/36)
> A = 112.923
Now with the full area, we can complete the first Area formula given at the top of this solution.
> A = pi * r^2
> 112.923 = 3.142 * r^2
> (112.923) / 3.142 = (3.142 * r^2) / 3.142
> 35.944 = r^2
> sqrt(35.944) = sqrt(r^2)
> 5.995 = r
I hoped this helped! If you ever want to make extra sure of your answers in future assignments, you should plug your final answer back into the equation and try to make your way back to ~59 cm^2. I've already checked the answer I've given, but if you'd like to as well, I'd encourage you to!
Have a good day!
