Question

Help ASAP!

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

Answer 1

B

Explanation:

`\boxed{area \: of \: sector = (1)/(2) {r}^(2) θ }`

Radius= diameter ÷2

r= 32 ÷2

r= 16

`(1)/(2) {r}^(2) θ = (512\pi)/(3)`

Substitute r= 16,

`(1)/(2) ( {16}^(2) )(θ) = (512\pi)/(3)`

`128 \: θ = (512\pi)/(3) \\ θ = (512\pi)/(3) / 128 \\ θ = (512\pi)/(384)`

Divide the denominator and numerator by 128:

`θ = (4\pi)/(3)`

Thus, the answer is B.