To find out the area that a center pivot irrigates, we can treat the area covered by the pivot as a circle. The radius of this circle is equal to half the length of the pivot.
Given that the length of the center pivot is 75 meters, the radius \( r \) would be:
\[ r = \frac{75m}{2} = 37.5m \]
The area \( A \) of a circle is calculated using the formula:
\[ A = \pi r^2 \]
Substituting the value of the radius into the formula:
\[ A = \pi (37.5)^2 \]
Calculating \( (37.5)^2 \):
\[ (37.5)^2 = 1406.25 \]
Now, substituting this value into the area formula:
\[ A = \pi \times 1406.25 \approx 3.14159 \times 1406.25 \approx 4420.5 , m^2 \]
Therefore, a center pivot that is 75 meters long can irrigate approximately 4420.5 square meters.
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