Solve the problem.
-An irrigation sprinkler in a field of lettuce sprays water over a distance of 35 feet as it rotates through an angle of 135°. What area of the field receives water? If necessary, round the answer to two decimal places.
A) $459.38 \mathrm { ft } ^ { 2 }$
B) $2,886.34 \mathrm { ft } ^ { 2 }$
C) $1,443.17 \mathrm { ft } ^ { 2 }$
D) $41.23 \mathrm { ft } ^ { 2 }$

Question

Solve the problem.
-An irrigation sprinkler in a field of lettuce sprays water over a distance of 35 feet as it rotates through an angle of 135°. What area of the field receives water? If necessary, round the answer to two decimal places. 
A) $459.38 \mathrm { ft } ^ { 2 }$
B) $2,886.34 \mathrm { ft } ^ { 2 }$
C) $1,443.17 \mathrm { ft } ^ { 2 }$
D) $41.23 \mathrm { ft } ^ { 2 }$

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $ \frac{\theta}{360} \times \pi r^2 $. Here, $ \theta = 135^\circ $ and $ r = 35 $ feet. Plugging in these values, the area is $ \frac{135}{360} \times \pi \times 35^2 \approx 1,443.17 \mathrm{ft}^2 $.

Solve the Problem 459.38ft2459.38 \mathrm { ft } ^ { 2 }459.38ft2

Solve the Problem $459.38 \mathrm { ft } ^ { 2 }$