Find a function that models the area A of a circle in terms of its circumference C.
A=πr² .... (1)
C=2πr, therefore r=C/(2π) ...(2)
Substitute (2) in (1) to get A in terms of C and π.
Sure, here's a clown-approved function for you:
A(C) = (C/2π)^2
This function takes the circumference C, divides it by 2π, and then squares the result to give you the area A. It's a simple yet amusing way to relate the area and circumference of a circle.
To find a function that models the area A of a circle in terms of its circumference C, we need to use the formula for the circumference and area of a circle.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
The area of a circle is given by the formula A = πr^2.
To express the area A in terms of the circumference C, we can eliminate the radius using the circumference formula.
From the circumference formula, we can solve for the radius r:
C = 2πr
r = C / (2π)
Substitute this expression for r in the area formula:
A = πr^2 = π(C / (2π))^2 = π(C^2 / (4π^2))
Simplifying further, we get:
A = C^2 / (4π)
Therefore, the function that models the area A of a circle in terms of its circumference C is A = C^2 / (4π).
To derive a function that models the area A of a circle in terms of its circumference C, we need to use mathematical relationships and formulas involving circles.
The circumference of a circle can be given by the formula C = 2πr, where r is the radius of the circle.
The area of a circle can be given by the formula A = πr^2.
Since we want to express the area A in terms of the circumference C, we can rearrange the first equation to solve for the radius r: r = C / (2π).
Substituting this value of r into the formula for the area, we can find a function that relates A and C:
A = πr^2 = π(C / (2π))^2 = πC^2 / (4π^2) = C^2 / (4π)
Hence, the function that models the area of a circle in terms of its circumference is:
A = C^2 / (4π)