Question

If the circumference of a circle is 2pi, what is the area?

Answer 1

The circumference of a circle is (pi) x (diameter).

The circumference of this circle is 2pi, so

2 pi = (pi) x (diameter).

So the diameter of this particular circle is 2,
Its radius is 1/2 of the diameter, so radius = 1.

The reason we need to know the radius is
because it's needed to find the area.

The area of any circle is (pi) x (radius squared).
For this particular circle ...

Area = (pi) x (1 squared) = pi square units .

Answer 2

Circumference of a circle= 2 * pi * r

Plug in what we know: 2pi = 2 * pi * r

Divide 2 pi to both sides: r = 1 (anything divided by itself is equal to 1)

Area = pi * r^2

Plug in what we know: A = pi * 1^2
A = pi * 1 ==> A = 1 pi

So the area is '1 pi' or just 'pi'.