Recall that the circumference of a circle is given by the following formula:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
We are given that:
[tex]79.63cm=2\pi r,[/tex]therefore:
[tex]r=\frac{79.63}{2*\pi}cm.[/tex]Now, the area of a circle is given by the following formula:
[tex]A=\pi r^2,[/tex]Therefore, the area of the hub cap is:
[tex]A=\pi *(\frac{79.63cm}{2})^2*\frac{1}{\pi^2}\approx505cm^2.[/tex]Answer:
[tex]\begin{equation*} 505cm^2. \end{equation*}[/tex]Given that the radius of the circle and the circumference are proportionally related, if the circumference is smaller then the radius is smaller. The area is proportionally related to the radius squared, therefore, a smaller circumference implies a smaller radius which implies a smaller area.
