Praxis Dashboard

The best estimate of the radius of the playground is 10 feet.

Using the area of 314 square feet, we can estimate the radius by applying the formula for the area of a circle, A = πr². Rearranging this formula gives us r = √(A/π). Plugging in the area, we approximate r as √(314/3.14), which results in a radius close to 10 feet.

A) 10 feet

Option A is correct as it accurately represents the estimated radius derived from the given area of 314 square feet. Calculating the radius using the formula r = √(314/π) results in approximately 10 feet, aligning perfectly with the value provided in this option.

B) 25 feet

Option B is incorrect because a radius of 25 feet would yield an area of about 1963.5 square feet (using A = πr²), which significantly exceeds the given area of 314 square feet. Thus, this option does not reflect a reasonable estimate based on the area provided.

C) 50 feet

Option C is also incorrect since a radius of 50 feet would correspond to an area of approximately 7854 square feet. This value is far greater than the 314 square feet specified in the question, making this estimate unrealistic.

D) 100 feet

Option D is incorrect as well. A radius of 100 feet would produce an area of about 31415.9 square feet, which is vastly larger than the area of 314 square feet. Therefore, this option is not a valid estimate based on the information given.

Conclusion

The correct answer of 10 feet is the only option that accurately estimates the radius given the area of the circular playground. All other options either significantly overestimate the radius or fail to align with the calculated area, demonstrating that they are not viable estimates in this context.