Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-$\mathrm { r } = 4.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians
A) $4.2 \mathrm { ft } 2$
B) $8.8 \mathrm { ft } ^ { 2 }$
C) $16.8 \mathrm { ft } ^ { 2 }$
D) $33.5 \mathrm { ft } ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a sector is given by $\frac{1}{2} r^2 \theta$. Substituting $r = 4.0$ and $\theta = \frac{2\pi}{3}$, the area is $\frac{1}{2} \times 4^2 \times \frac{2\pi}{3} = \frac{1}{2} \times 16 \times \frac{2\pi}{3} = \frac{32\pi}{6} \approx 16.8 \mathrm{ft}^2$.

Find the Area of a Sector of a Circle Having θ\thetaθ

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