Question

three students tried to calculate the circumference. order their answers from farthest from the exact circumferen to closest to the exact circumference. 10π units 31.4 units 31.4π units

Explanation:

Step1: Calculate the exact circumference

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 5\) units, then \(C=2\pi\times5 = 10\pi\) units. Approximating \(\pi\approx3.14\), we get \(C\approx10\times3.14=31.4\) units.

Step2: Analyze each value

• For \(31.4\pi\) units: If \(\pi\approx3.14\), then \(31.4\pi\approx31.4\times3.14 = 98.596\) units. The difference from the exact value \(10\pi\approx31.4\) is \(|98.596 - 31.4|=67.196\) (using \(\pi\approx3.14\) for comparison).
• For \(10\pi\) units: This is the exact formula - based value (no approximation error in terms of the formula \(C = 2\pi r\)).
• For \(31.4\) units: Using \(\pi\approx3.14\), \(10\pi\approx31.4\), so the difference from the value calculated using the formula \(C = 2\pi r\) (with \(\pi\) approximated) is very small (the error comes from the approximation of \(\pi\) itself, and if we consider the formula - based exact form \(10\pi\), when \(\pi\) is approximated as \(3.14\), \(10\pi\approx31.4\)).

Answer:

FARTHEST FROM EXACT CIRCUMFERENCE: \(31.4\pi\) units, MIDDLE: \(10\pi\) units, CLOSEST TO EXACT CIRCUMFERENCE: \(31.4\) units.