Question

In a circle with a diameter of 32, the area of a sector is 512π 3 . the measure of the angle of the sector, in radians, is

Answer 1

Answer: $4\pi\text{ radians}$

Step-by-step explanation:

The formula to calculate the area of a sector with central angle 'x' and radius 'r' is given by ;-

$\text{ Area of sector}=\dfrac{x}{2}\times r^2$

Given: The diameter of circle= $\dfrac{d}{2}=\dfrac{32}{2}=16\text{ units}$

Area of sector = $512\pi\text{ units}^3$

Let x be the central angle of the given circle, then

$\Rightarrow\ 512\pi=\dfrac{x}{2}\times (16)^2\\\\\Rightharrow\ x=\dfrac{512\pi\times2}{16^2}\\\\\Rightharrow\ x=4\pi\text{ radians}$

Answer 2

4π/3 hope this helps