elizabeth700
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In a circle with a diameter of 32, the area of a sector is 512(pi)/3. The measure of the angle of a sector in radians is

A.) π/3
B.) 4π/3
C.)16π/3
D.)64π/3

Sagot :

Leora03

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.

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