The circumference of a circle is directly proportional to its diameter or radius, while the area of a circle is directly proportional to the square of its diameter or radius. In equation form:
Circumference = 2πr = πd
Area = πr^2 = (π/4)d^2
Correct expression that shows the relationship between the circumference and the area of a circle
3 answers
or to combine them for relationship:
Circumference = C = 2πr = πd
so
d = C / π
and d^2 = C^2 / π^2
Area = A = πr^2 = (π/4)d^2 = (π/4)C^2 / π^2
A = C^2 / (4 π)
Circumference = C = 2πr = πd
so
d = C / π
and d^2 = C^2 / π^2
Area = A = πr^2 = (π/4)d^2 = (π/4)C^2 / π^2
A = C^2 / (4 π)
Therefore, the relationship between the circumference and the area of a circle is that the area is directly proportional to the square of the circumference, with a constant of proportionality of 1/4π.