Question

The circumference of a circle is 16pi. what is th circles area? leave your answer in terms of pi.

Answer 1

The circumference of a circle is C=16π, using this information you have to determine the area of the circle.

The circumference of a circle can be calculated as pi multiplied by the diameter of the circle:

`C=d\pi`

From this formula we can calculate the diameter of the circle as follows:

`\begin{gathered} (C)/(\pi)=(d\pi)/(\pi) \\ d=(C)/(\pi) \end{gathered}`

If C=16π, then the diameter is:

`\begin{gathered} d=(16\pi)/(\pi) \\ d=16 \end{gathered}`

Once we know the diameter of the circle, we can calculate the area.

The area of the circle can be calculated using the following formula

`A=\pi r^2`

If the diameter of the circle is 16 units, then the radius is r=8 units (since the radius is half the diameter)

`\begin{gathered} A=\pi r^2 \\ A=\pi(8)^2 \\ A=64\pi \end{gathered}`

The area of the circle is 64π units²