Correct expression that shows the relationship between the circumference and the area of a circle
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)
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
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.
The correct expression that shows the relationship between the circumference and the area of a circle is:
C = 2πr
and
A = πr^2
In these expressions, C represents the circumference of the circle, A represents the area of the circle, and r represents the radius of the circle.
To understand how these expressions relate, we need to know that the circumference of a circle is the distance around the outside edge, and the area of a circle is the measure of the region enclosed by the circle.
The expression C = 2πr tells us that the circumference of a circle is equal to twice the value of pi (π) multiplied by the radius (r). This means that the circumference increases as the radius increases since it is directly proportional to the radius.
On the other hand, the expression A = πr^2 informs us that the area of a circle is equal to the value of pi (π) multiplied by the square of the radius (r^2). In this case, the area increases as the radius increases, but it does so in a squared manner. This means that as the radius doubles, the area quadruples.
So, these expressions illustrate that both the circumference and the area of a circle are influenced by the radius, but in different ways. The circumference is directly proportional to the radius, while the area is proportional to the square of the radius.