An irrigation pivot makes a circle with a radius of about 400 meters. Which of the following values is closest to the area, in square meters, of the circle?

Rationale

The area of the circle made by the irrigation pivot is approximately 502,700 square meters.

To find the area of a circle, the formula used is A = πr². Given a radius of 400 meters, the area calculates to approximately 502,654 square meters when using π ≈ 3.14, which rounds to 502,700 square meters.

A (1,300) YOUR ANSWER

This value is significantly lower than the calculated area. The area of a circle with a radius of 400 meters is much larger than 1,300 square meters, which would correspond to a very small radius—far less than the given dimension.

B (2,500) YOUR ANSWER

Similarly to choice A, this option does not reflect the size of the circle. An area of 2,500 square meters would suggest an even smaller radius, around 28 meters, which is not applicable for the given radius of 400 meters.

C (160,000) YOUR ANSWER

While closer to a reasonable area than A or B, 160,000 square meters still underestimates the area significantly. Calculating the area of a circle with a radius of 400 meters yields a result much larger than this figure.

D (502,700) CORRECT

This is the correct answer, as it accurately represents the area calculated using the formula A = πr² with r = 400 meters. The computed area is approximately 502,654 square meters, which rounds to 502,700 square meters.

E (1,579,100) YOUR ANSWER

This value is far too high for the area of a circle with a 400-meter radius. An area of this size would correspond to a radius of about 564 meters, which exceeds the given dimension of 400 meters.

Conclusion

The area of the circle formed by the irrigation pivot using a radius of 400 meters is approximately 502,700 square meters, derived from the area formula for circles. Other choices provided either underestimate or overestimate the area, confirming that D is the closest and correct value based on the calculations.