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 is approximately 502700 square meters.

Using the formula for the area of a circle, A = πr², where r is the radius, we can calculate the area. With a radius of 400 meters, the area is approximately 502,654 square meters when using π ≈ 3.14, making 502700 the closest value.

A (1300) YOUR ANSWER

This figure is far too small to represent the area of a circle with a radius of 400 meters. Using the area formula, the calculated area is significantly larger than this value, indicating a misunderstanding of the geometric properties involved.

B (2500) YOUR ANSWER

While this number is larger than 1300, it still falls short of the actual area as computed from the radius. The area of a circle with a substantial radius like 400 meters will be in the hundreds of thousands, not just a couple of thousand square meters.

C (160000) YOUR ANSWER

This option is closer to the correct area but still does not accurately reflect the calculation. The actual area calculated is approximately 502,654 square meters, which is much greater than 160,000, highlighting a miscalculation of the area formula.

D (502700) CORRECT

This value is the closest approximation to the calculated area of the circle, which is about 502,654 square meters. It accurately reflects the geometric properties of a circle with a radius of 400 meters.

E (1579100) YOUR ANSWER

This figure significantly exceeds the actual area of the circle, indicating a misunderstanding in the calculation. The area cannot reach this high value given a radius of 400 meters, which further emphasizes the need for proper application of the area formula.

Conclusion

The area of a circle is determined by the formula A = πr², and for a circle with a radius of 400 meters, the area is approximately 502,654 square meters. Among the provided options, 502700 is the closest estimate, while all other choices reflect either significant underestimations or overestimations of the area. Understanding these calculations is essential in accurately determining geometric properties.