Question

Express the area A of circle as a function of its circumference C.

Answer 1

If C is the circumference and r is the radius of the circle, then C = 2πr

∴ r = `"C"/(2pi)`

∴ the area A of the circle is given by

A = πr²

= `pi("C"/(2pi))^2`

= `"C"^2/(4pi)`

∴ A = `"C"^2/(4pi)`