11. 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?
Answer: D
The area of the circle is approximately 502,700 square meters.
The area of a circle can be calculated using the formula A = πr², where r is the radius. Given a radius of 400 meters, the area is approximately 502,700 square meters.
A) 1,300
This value is significantly lower than the actual area of the circle. Using the formula A = πr² with a radius of 400 meters clearly shows that the area cannot be as small as 1,300 square meters.
B) 2,500
Similar to Option A, this value is also far too low. The area of the circle exceeds 2,500 square meters, as calculations based on the given radius indicate a much larger area.
C) 160,000
While this value is closer to the correct area than Options A and B, it still underestimates the size of the circle. The actual calculation shows that the area is significantly larger than 160,000 square meters.
D) 502,700
This value accurately reflects the area of the circle calculated using the formula A = πr² with a radius of 400 meters. It is the closest option to the calculated area.
E) 1,579,100
This option is excessively high and does not align with the area calculated for a circle with a 400-meter radius. The actual area is much smaller than this value.
Conclusion
The correct answer, 502,700 square meters, is derived from the area formula for a circle, confirming its validity. All other options either underestimate or overestimate the area, demonstrating a clear understanding of the geometric principles involved in calculating the area of a circle.