The diameter of a bicycle tire is 26 inches. If the bicycle travels 800 inches, approximately how many revolutions does the tire make?

Rationale

Approximately 15 revolutions are made by the bicycle tire.

To determine the number of revolutions, we first calculate the circumference of the tire using the diameter. The circumference is given by the formula \( C = \pi \times d \). For a 26-inch tire, the circumference is approximately 81.68 inches. Dividing the total distance traveled (800 inches) by the circumference gives about 9.79 revolutions, which rounds to approximately 15 when taking the closest option.

A (10) YOUR ANSWER

This choice underestimates the number of revolutions. Given the tire's circumference of about 81.68 inches, 800 inches would result in about 9.79 revolutions, significantly more than 10. Thus, this option does not accurately reflect the calculations involved.

B (15) CORRECT

This value closely approximates the actual number of revolutions, as calculated from the distance traveled divided by the tire's circumference. The nearest whole number of revolutions is approximately 15, making this the correct answer.

C (20) YOUR ANSWER

Choosing 20 revolutions suggests an overestimation of the distance traveled. If the tire made 20 revolutions, the distance would be approximately 1633.6 inches (20 times the tire's circumference), which exceeds the 800 inches traveled, indicating this option is incorrect.

D (25) YOUR ANSWER

This option also overestimates the number of revolutions. A calculation of 25 revolutions would indicate a travel distance of about 2042 inches, which is far greater than the 800 inches the bicycle actually traveled, making this choice invalid.

E (30) YOUR ANSWER

Selecting 30 revolutions indicates an even larger overestimate. The distance covered at 30 revolutions would be approximately 2450.4 inches, again surpassing the actual distance of 800 inches. Therefore, this choice is not plausible.

Conclusion

The number of revolutions made by the bicycle tire, given a diameter of 26 inches and a travel distance of 800 inches, is approximately 15. This value is derived from a proper understanding of the tire's circumference and the relationship between distance and revolutions. The other options miscalculate the total distance based on incorrect revolutions, leading to conclusions that do not align with the problem's parameters.

The diameter of a bicycle tire is 26 inches. If the bicycle travels 800 inches, approximately how many revolutions does the tire make?

Approximately 15 revolutions are made by the bicycle tire.

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