The relationship between the area of a circle and its radius is governed by the mathematical formula for the area: A = πr², where A represents the area, r the radius, and π (pi) is approximately equal to 3.14159.
To find a function that models the radius r in terms of the area A, we start with the area formula:
A = πr²We can solve for r by following these steps:
- Isolate the term with r²:
A = πr²
Divide both sides by π:
r² = A / π - Take the square root of both sides to solve for r:
r = √(A / π)
Thus, the function that models the radius r of a circle in terms of its area A is:
r(A) = √(A / π)This function allows you to compute the radius of a circle if you know its area. For example, if the area of a circle is 50 square units:
A = 50You can calculate the radius as follows:
r = √(50 / π) ≈ 3.99In short, the radius r of a circle can be efficiently determined from its area A using the formula r = √(A / π), making it easier to visualize the dimensions of the circle given its area.