A square wheat field is watered by a center pivot irrigation system with a 34-foot radius. What area of the field will not be irrigated?

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Answer 1 · 2017-12-06T04:41:41

Assuming the length and the width of the field is the same as the diameter of the center pivot irrigation system see a solution process below:

First, we need to determine the area of the square wheat field:

If the length of a side of the field is the same as the diameter of the irrigation system, then the side of the wheat field is:

#s = d = 2r = 2 * 34"ft" = 68"ft"#

The area of a square is: #A_s = s^2#

Substituting gives:

#A_s = (68"ft")^2#

#A_s = 4624"ft"^2#

The area of a circle is:

#A_c = pir^2#

Substituting gives:

#A_c = pi(34"ft")^2#

#A_c = pi1156"ft"^2#

The area of the field not covered by the irrigation system is the area of the circle subtracted from the area of the square:

#4624"ft"^2 - pi1156"ft"^2#

Substituting #3.14# as an approximation of #pi# gves:

#4624"ft"^2 - (3.14 xx 1156)"ft"^2#

#4624"ft"^2 - 3629.84"ft"^2#

#994.16"ft"^2#

Approximately #994.6# square feet will not be covered by the irrigation system.