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:
[tex]C=d\pi[/tex]From this formula we can calculate the diameter of the circle as follows:
[tex]\begin{gathered} \frac{C}{\pi}=\frac{d\pi}{\pi} \\ d=\frac{C}{\pi} \end{gathered}[/tex]If C=16π, then the diameter is:
[tex]\begin{gathered} d=\frac{16\pi}{\pi} \\ d=16 \end{gathered}[/tex]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
[tex]A=\pi r^2[/tex]If the diameter of the circle is 16 units, then the radius is r=8 units (since the radius is half the diameter)
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(8)^2 \\ A=64\pi \end{gathered}[/tex]The area of the circle is 64π units²
