Question

1. if the central angle of a sector is $2\pi/3$ radians and the radius is 8 meters, what is the sector area?

a. $16\pi$ square meters
b. $26\pi/3$ square meters
c. $64\pi/3$ square meters
d. $32\pi$ square meters

Explanation:

Step1: Recall sector area formula

Area = $\frac{1}{2}r^2\theta$ (θ in radians)

Step2: Substitute values

$r=8$, $\theta=\frac{2\pi}{3}$ → Area = $\frac{1}{2}(8)^2(\frac{2\pi}{3})$

Step3: Calculate

$\frac{1}{2}×64×\frac{2\pi}{3} = \frac{64\pi}{3}$

Answer:

c. 64π/3 square meters