A circular playground has an area of 314 square feet. Which of the following is the best estimate of the radius, in feet, of the playground?
10 feet is the best estimate of the radius of the playground.
The area of a circle is calculated using the formula A = πr². Given the area of 314 square feet, we can estimate the radius by rearranging the formula to r = √(A/π). Using π ≈ 3.14, we find that the radius is approximately 10 feet.
This choice is the best estimate for the radius based on the area provided. Using the area formula, we calculate the radius: r = √(314/π) which approximates to √(100) = 10 feet. Thus, this answer accurately reflects the given area of the playground.
If the radius were 25 feet, the area would be A = π(25)² = π(625) ≈ 1963.5 square feet, which is significantly larger than the given area of 314 square feet. This choice greatly overestimates the required radius.
A radius of 50 feet would result in an area of A = π(50)² = π(2500) ≈ 7850 square feet. This is far beyond the specified area of 314 square feet, making this choice not reasonable at all.
With a radius of 100 feet, the area would be A = π(100)² = π(10000) ≈ 31415.9 square feet, which is excessively larger than the area of 314 square feet. Similar to option C, this choice is not plausible.
The radius of 10 feet is the only choice that accurately estimates the radius of the circular playground with an area of 314 square feet. The calculations for the other options reveal they significantly exceed the area, demonstrating that 10 feet is not only the most accurate choice but also the only reasonable estimate.
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