Question

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Answer 1

Answer:

B

Step-by-step explanation:

$\boxed{area \: of \: sector = \frac{1}{2} {r}^{2} θ }$

Radius= diameter ÷2

r= 32 ÷2

r= 16

$\frac{1}{2} {r}^{2} θ = \frac{512\pi}{3}$

Substitute r= 16,

$\frac{1}{2} ( {16}^{2} )(θ) = \frac{512\pi}{3}$

$128 \: θ = \frac{512\pi}{3} \\ θ = \frac{512\pi}{3} \div 128 \\ θ = \frac{512\pi}{384}$

Divide the denominator and numerator by 128:

$θ = \frac{4\pi}{3}$

Thus, the answer is B.