Answer: [tex]4\pi\text{ radians}[/tex]
Step-by-step explanation:
The formula to calculate the area of a sector with central angle 'x' and radius 'r' is given by ;-
[tex]\text{ Area of sector}=\dfrac{x}{2}\times r^2[/tex]
Given: The diameter of circle= [tex]\dfrac{d}{2}=\dfrac{32}{2}=16\text{ units}[/tex]
Area of sector = [tex]512\pi\text{ units}^3[/tex]
Let x be the central angle of the given circle, then
[tex]\Rightarrow\ 512\pi=\dfrac{x}{2}\times (16)^2\\\\\Rightharrow\ x=\dfrac{512\pi\times2}{16^2}\\\\\Rightharrow\ x=4\pi\text{ radians}[/tex]
