For this problem, we are given the measurement of the circumference of a circle. We need to determine the area of this circle.
The expression for the circumference is shown below:
[tex]C=2\pi r[/tex]The expression for the area is:
[tex]A=\pi r^2[/tex]We can use the first expression and the given circumference to determine the radius:
[tex]\begin{gathered} 79.63=2\cdot3.14\cdot r\\ \\ r=\frac{79.63}{2\cdot3.14}=\frac{79.63}{6.28}=12.68\text{ cm} \end{gathered}[/tex]The radius is 12.68 cm. We need to determine the area:
[tex]A=3.14\cdot12.68^2=3.14\cdot160.78=504.86\text{ square cm}[/tex]The area for the hub cap is 504.86 square cm.
