Solve the problem.
-A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, $\theta = 32 ^ { \circ }$ and the radius, $r = 151$ meters. Round to the nearest whole number.
A) $6367 \mathrm {~m} ^ { 2 }$
B) $84 \mathrm {~m} ^ { 2 }$
C) $42 \mathrm {~m} ^ { 2 }$
D) $12,734 \mathrm {~m} ^ { 2 }$

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 $\theta$ is in radians. First, convert the central angle to radians: $32^\circ = \frac{32\pi}{180} = \frac{8\pi}{45}$ radians. Then, calculate the area: $A = \frac{1}{2} \times 151^2 \times \frac{8\pi}{45} \approx 6367 \, \text{m}^2$.

Solve the Problem θ=32∘\theta = 32 ^ { \circ }θ=32∘ And the Radius

Solve the Problem $\theta = 32 ^ { \circ }$ And the Radius