Question

Question

Which of the following expressions correctly shows the relationship between the circumference and the area of a circle?(1 point)
Responses

C2=4πA
upper C squared equals 4 pi upper A

A=πr2
upper A equals pi r squared

Cd=π
Start Fraction upper C over d End Fraction equals pi

C=2πr
upper C equals 2 pi r
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Answer 1

The expressions you provided relate to the properties of a circle. Here are the correct relationships:

1. C² = 4πA: This expression is true, as it expresses a relationship between the circumference (C) and area (A) of a circle, but it's not the most direct formulation of the basic formulas.

2. A = πr²: This is the standard formula for the area (A) of a circle given its radius (r).

3. C/d = π: This is also true, as it represents the ratio of the circumference (C) to the diameter (d) of a circle, which is always π.

4. C = 2πr: This is the standard formula for the circumference (C) of a circle given its radius (r).

Among these, options 2 and 4 are the most direct and commonly used formulas for area and circumference. The option that directly shows the relationship between circumference and area is the first one (C² = 4πA), even though it is less commonly presented.

If the question seeks the most fundamental or recognized formulas, C = 2πr and A = πr² would be primary choices.

However, for the specific expression relating circumference to area in terms of equalities, C² = 4πA is correct.