A child rolls a ball on a level floor 3.1 m to another child. If the ball makes 12.0 revolutions, what is its diameter?

검증된 단계별 안내

Determine the total distance traveled by the ball, which is given as 3.1 m.

Recall the relationship between the distance traveled by a rolling object and the number of revolutions it makes: \( d = n \cdot C \), where \( d \) is the distance, \( n \) is the number of revolutions, and \( C \) is the circumference of the ball.

The circumference \( C \) of a circle is related to its diameter \( D \) by the formula \( C = \pi D \). Substitute this into the distance formula: \( d = n \cdot \pi D \).

Rearrange the formula to solve for the diameter \( D \): \( D = \frac{d}{n \cdot \pi} \).

Substitute the given values: \( d = 3.1 \; \text{m} \), \( n = 12.0 \), and \( \pi \approx 3.1416 \) into the formula to calculate \( D \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Circumference of a Circle

The circumference of a circle is the distance around it, calculated using the formula C = πd, where d is the diameter. In this problem, knowing the circumference is essential to relate the number of revolutions the ball makes to its diameter.

Revolutions and Distance

One complete revolution of a circular object corresponds to a distance equal to its circumference. Therefore, if the ball makes 12.0 revolutions, the total distance traveled can be expressed as D = number of revolutions × circumference, which is crucial for determining the diameter.

Linear Distance Measurement

Linear distance measurement refers to the straight-line distance between two points. In this scenario, the ball rolls a total distance of 3.1 m, which is the key measurement needed to calculate the diameter of the ball based on the revolutions it completes.