14. A lawn sprinkler located at the corner of a yard is set to rotate through 90^circ and project water out 30 feet. What area of the lawn is watered by the sprinkler? ROUND TO THE NEAREST HUNDREDTH. SA=(pi r^2x)/(360)

To calculate the area of the lawn watered by the sprinkler, we use the formula for the sector area of a circle:<br /><br />\[<br />SA = \frac{\pi r^2 x}{360}<br />\]<br /><br />Where:<br />- \(r = 30\) feet (radius of the sprinkler's reach),<br />- \(x = 90^\circ\) (the angle of rotation),<br />- \(\pi \approx 3.1416\).<br /><br />Substitute the values into the formula:<br /><br />\[<br />SA = \frac{\pi (30)^2 (90)}{360}<br />\]<br /><br />1. Calculate \(30^2\):<br />\[<br />30^2 = 900<br />\]<br /><br />2. Multiply \(900 \times 90\):<br />\[<br />900 \times 90 = 81,000<br />\]<br /><br />3. Divide \(81,000\) by 360:<br />\[<br />\frac{81,000}{360} = 225<br />\]<br /><br />4. Multiply by \(\pi\):<br />\[<br />225 \times \pi \approx 225 \times 3.1416 = 706.86<br />\]<br /><br />Thus, the area of the lawn watered by the sprinkler is approximately **706.86 square feet**.