How do you find the area radius and diameter with just the circumference?

Answer 1

Given that the circumference of any circle is 2 * pi * r, where pi is the mathematical constant (~3.14) and r is the radius, solving for the radius is quite simple.

we'll call the circumference c:

c = 2*pi*r

divide both sides by 2*pi:

c/(2pi) = r

and then the diameter is just 2 * radius.

Area = pi*(r)^2 = pi*(c/(2*pi))^2 = (c^2)/(4*pi)

(~ denotes approx. value)

Quick example:

So if a circle has a circumference of 30cm:

30 cm= 2 * pi * r

r = (30cm)/(2*pi)

r = (30cm)/(2*3.14) = ~4.78 cm

diameter = 2 * ~4.78 cm = ~9.56 cm

area = (30 cm)^2 / (4* ~3.14) = ~71.66 cm^2

c = 30 cm, r = ~4.78 cm, d = ~9.56 cm