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.
-A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, $\theta = 20 ^ { \circ }$ and the radius, $r = 160$ meters. Round to the nearest whole number.
A) $28 m ^ { 2 }$
B) $4468 \mathrm {~m} ^ { 2 }$
C) $56 \mathrm {~m} ^ { 2 }$
D) $8936 \mathrm {~m} ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $A = \frac{1}{2} r^2 \theta$, where $A$ is the area, $r$ is the radius, and $\theta$ is the central angle in radians. To use the formula, first convert the central angle from degrees to radians: $\theta = 20^\circ = \frac{20\pi}{180} = \frac{\pi}{9}$ radians. Then, $A = \frac{1}{2} \times 160^2 \times \frac{\pi}{9} \approx 4468.1 \mathrm{~m}^2$, which rounds to $4468 \mathrm{~m}^2$.

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

Find the Area of a Sector of a Circle Having $\theta$