Which of the following is the circumference of a circle with a radius of 5 inches? Note: Use pi ~ 3.14.

Rationale

The circumference of a circle with a radius of 5 inches is 31.4 inches.

To calculate the circumference of a circle, the formula \(C = 2\pi r\) is used. Substituting the radius of 5 inches and using \(\pi \approx 3.14\), the calculation yields \(C = 2 \times 3.14 \times 5 = 31.4\) inches.

A (15.7 inches) YOUR ANSWER

This choice is calculated as if the circumference were derived from a radius of 2.5 inches instead. Specifically, \(2 \times 3.14 \times 2.5 = 15.7\) inches. This value does not correspond to a radius of 5 inches, making it incorrect.

B (78.5 inches) YOUR ANSWER

This answer results from incorrectly applying the formula, possibly by miscalculating the radius or mistakenly multiplying by an extraneous factor. The correct calculation for a radius of 5 inches yields 31.4 inches, so this option is significantly larger and thus incorrect.

C (10 inches) YOUR ANSWER

This value suggests a misunderstanding of the circumference formula. It appears to be derived from a very small radius or an erroneous calculation. The radius of 5 inches clearly leads to a much larger circumference than 10 inches, making this choice incorrect.

D (31.4 inches) CORRECT

This is the correct answer, derived from the accurate application of the circumference formula. By substituting the radius and using \(\pi \approx 3.14\), the result confirms the calculation as correct.

Conclusion

The circumference of a circle is fundamentally determined by its radius and the mathematical constant \(\pi\). For a circle with a radius of 5 inches, the accurate circumference calculated as \(31.4\) inches demonstrates the essential relationship between radius and circumference in circular geometry. Other options either misapply the formula or reflect incorrect interpretations of the radius, highlighting the importance of precise calculations in mathematics.

Which of the following is the circumference of a circle with a radius of 5 inches? Note: Use pi ~ 3.14.

The circumference of a circle with a radius of 5 inches is 31.4 inches.

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