To answer this question, we need to use scientific notation for the value of the radius as follows:
[tex]0.00678=0.00678\cdot\frac{10^3}{10^3}=6.78\cdot10^{-3}[/tex]
Then, using the formula for the area of a circle, we have:
[tex]A_{\text{circle}}=\pi\cdot(6.78\cdot10^{-3})^2=\pi\cdot(6.78)^2\cdot(10^{-3})^2=\pi\cdot45.9684\cdot10^{-6}in^{}[/tex]
Then, we have:
[tex]A_{\text{circle}}=\pi\cdot45.9684\cdot10^{-6}\cdot\frac{10}{10}=\pi\cdot4.59684\cdot10^{-6}\cdot10=4.59684\cdot10^{-5}\pi in^2[/tex]
Therefore, the answer to this question is the first option: 4.59684 * 10^-5 pi square inches.
