22. 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 502700 square meters.
To find the area of a circle, the formula A = πr² is used, where r is the radius. With a radius of 400 meters, the area calculates to about 502700 square meters.
A) 1300
This value is significantly lower than the actual area of the circle. Using the formula A = πr², even a small radius like 1 meter yields an area of approximately 3.14 square meters, indicating that 1300 is not a plausible area for a circle with a 400-meter radius.
B) 2500
While this value is larger than 1300, it is still far too small for the area of a circle with a radius of 400 meters. The area calculated using the circle area formula shows that 2500 square meters is inadequate compared to the actual area.
C) 160000
This option is closer than the previous values but still falls short of the correct calculation. The area of a circle with a radius of 400 meters is much larger than 160000 square meters, as verified by applying the area formula.
D) 502700
This is the correct calculation for the area of the circle with a radius of 400 meters. When applying the formula A = π(400)², the result is approximately 502700 square meters, making this option accurate.
E) 1579100
This value is excessively high for the area of a circle with a 400-meter radius. The area calculation shows that it is more than three times larger than the actual area, confirming it as incorrect.
Conclusion
The correct answer, 502700 square meters, is derived directly from the area formula for circles. Other options, whether too low or excessively high, fail to represent the area accurately based on the given radius, demonstrating that D is the only plausible choice.