The expressions below show different relationships involving the circumference \( C \) and area \( A \) of a circle. Here's an analysis of the options:
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C² = 4πA - This is a rearranged relationship, but it is not a standard equation that defines the relationship between circumference and area in a clear way.
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C/d = π - This expression states that the ratio of circumference \( C \) to diameter \( d \) is equal to \( \pi \), which is a correct and known relationship.
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C = 2πr - This equation states that the circumference \( C \) is equal to \( 2\pi \) times the radius \( r \). This is a standard formula for the circumference of a circle.
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A = πr² - This equation states that the area \( A \) of a circle is equal to \( \pi \) times the radius squared. This is also a standard formula for the area of a circle.
The correct expression showing the relationship between the circumference and the area of a circle is:
C = 2πr (this directly relates circumference to radius, which is fundamentally important in understanding circles)
However, A = πr² is also fundamental as it defines how area relates to radius in a circle.
If you are looking for the most direct answer focused on the circumference itself, the best choice would be:
C = 2πr.