How to find the area of a circle with the circumference

The circumference is the perimeter of a circle. It is a length and so is measured in \(mm\), \(cm\), \(m\) or \(km\).

An area is measured in square units: \(mm^{2}\), \(cm^{2}\), \(m^{2}\) or \(km^{2}\)

All of these calculations will involve the use of \(\pi\)(Pi)

Some calculators have a \(\pi\) button but you can also use substitute \(\pi = 3.14\).

However the answers for these two ways of dealing with \(\pi\) are slightly different.

Both ways are allowed, so if your answer is slightly different from the answer given for a question then this is acceptable as long as you have rounded correctly for your method.

Circumference of a circle

For any circle with diameter, \(d\), the circumference, \(C\), is found by using the formula \(C = \pi d\)

For this circle:

\[C = \pi d\]

\[= \pi \times 8\]

\[= 25.13cm\]

Remember that, for any circle, the diameter is twice the radius, or \(d = 2r\).

For this circle:

\[Diameter = 2r\]

\[=2\times 3\]

\[=6cm\]

\[C = \pi d\]

\[=\pi\times 6\]

\[= 18.85cm\]

Area of a circle

For any circle with radius, \(r\), the area, \(A\), is found using the formula \(A = \pi {r^2}\).

For this circle:

\[A = \pi {r^2}\]

\[= \pi \times 3 \times 3\]

\[= 28.27c{m^2}\]