Answer:
B
Step-by-step explanation:
[tex]\boxed{area \: of \: sector = \frac{1}{2} {r}^{2} θ }[/tex]
Radius= diameter ÷2
r= 32 ÷2
r= 16
[tex] \frac{1}{2} {r}^{2} θ = \frac{512\pi}{3} [/tex]
Substitute r= 16,
[tex] \frac{1}{2} ( {16}^{2} )(θ) = \frac{512\pi}{3} [/tex]
[tex]128 \: θ = \frac{512\pi}{3} \\ θ = \frac{512\pi}{3} \div 128 \\ θ = \frac{512\pi}{384} [/tex]
Divide the denominator and numerator by 128:
[tex]θ = \frac{4\pi}{3} [/tex]
Thus, the answer is B.
