Question

A water sprinkler sprays water over a distance of 36 yards while rotating through an angle of 125°. What area of lawn receives water? Round to the nearest integer as needed.

Answer 1

Answer:

1413 square yards of lawn receives water.

Step-by-step explanation:

We are given the following in the question:

Radius of garden, r = 36 yards

Rotating angle, $\theta$  = $125^\circ$

First converts the given angle measure in radians.

$\text{Radians} = \dfrac{\pi}{180}\times \theta$

Thus, the rotating angle in radians is:

$\dfrac{\pi}{180}\times 125 = 2.18\text{ Radians}$

Area of lawn =

$\displaystyle\frac{1}{2}r^2 \times \text{Radian measure of angle}\\\\=\frac{1}{2}(36)^2\times 2.18 = 1412.64 \approx 1413\text{ square yards}$

Thus, 1413 square yards of lawn receives water.