Question

Farmer Grainger’s square plot yields 350 bushels of grain. To increase the yield, Grainger invests in a circular sprinkler pivot to irrigate a square plot of land. When he places the sprinkler at the center of the field and stretches the arm to half the field’s length, he estimates that the sprinkler will triple the yield over the irrigated circular area, even though some land will not be irrigated.

(a) What is the projected yield of the circular area once the pivot is installed?
(b) Farmer Grainger wonders if he could increase his yield by placing the sprinkler so that the circular pivot’s center is at one corner of the square plot of land, thereby extending the watering arm to the length of the field. Is this a better configuration than the configuration in part (a) above?

Answer 1

To calculate the projected yield of the circular area, find the area of the circular region and triple it. Compare the yields of different configurations by calculating the area of the circular region in each configuration.

Step-by-step explanation:

To calculate the projected yield of the circular area once the pivot is installed, we need to find the area of the circular region and then triple it. The area of a circle is given by the formula A = πr^2, where r is the radius. In this case, the radius is half the length of the field. Once we find the area of the circle, we triple it to get the projected yield.

To determine if placing the sprinkler at the corner of the square plot is a better configuration, we need to compare the areas of the circular regions in both configurations. We can calculate the area of the circular region in this configuration using the same formula as before. By comparing the projected yields of both configurations, we can determine which one is better.