Q. 95 - Precalculus Enhanced with Graphing Utilities

Question

A water sprinkler sprays water over a distance of $30$feet while rotating through an angle of ${135}^{\circ }$

Step-by-Step Solution

Answer

The area of the lawn that receives the water from the sprinkler is $1060.29f{t}^2$

Step 1. Given information

water sprinkler sprays water over a distance of $30$feet while rotating through an angle of ${135}^{\circ }$ 

Step 2. Used formulae

The area of a circle with radius $r$ and angle $\theta$ is $A=\frac{1}{2}{r}^2\theta$

Step 3. Calculation

${135}^{\circ }=135·\frac{\mathrm{\pi }}{180}=\frac{3\mathrm{\pi }}{4}$ 

For the given problem, we substitute and the area is obtained as 

$A=\frac{1}{2}·{\left(30\right)}^2·\frac{3\mathrm{\pi }}{4}=90\mathrm{\pi }\approx 1060.29f{t}^2$