Answer:
The radius is just under 4 cm.
Explanation:
The central angle for the entire circle is 360 degrees.
The fraction (89/360)(total circle area) = 12.36m^2.
Solving for the total circle area, we get (360/89)(12.36m^2) = 50 cm^2.
Area of a circle (in general) is A = πr²
Here we know A and π and must find r² and then r:
A
A = πr² becomes r² = ----------
π
Here, r² = 50 cm^2 / 3.14 = 15.92 cm^2
and r = square root of r² = 3.99, or approximately 4 cm