Answer:
1320336992.2512 m²
1320.33 kilometers or 509.79 miles
Explanation:
Energy transferred by the sun
[tex]W=0.24\times 1\times 10^3=240\ W/m^2[/tex]
Energy required by the United States is [tex]1\times 10^{19}\ J/yr[/tex] (assumed)
Power
[tex]P=\frac{E}{t}\\\Rightarrow P=\frac{1\times 10^{19}}{365.25\times 24\times 3600}\\\Rightarrow P=316880878140.2895\ W[/tex]
Area
[tex]A=\frac{P}{W}\\\Rightarrow A=\frac{316880878140.2895}{240}\\\Rightarrow A=132033699.2512\ m^2[/tex]
Area of the solar collector would be 1320336992.2512 m²
Converting to km²
[tex]1\ m^2=\frac{1}{1000\times 1000}\ km^2[/tex]
[tex]1320336992.2512\ m^2=1320336992.2512\times \frac{1}{1000\times 1000}\ km^2=1320.33\ km^2[/tex]
Converting to mi²
[tex]1\ m^2=\frac{1}{1609.34\times 1609.34}\ mi^2[/tex]
[tex]1320336992.2512\ m^2=1320336992.2512\times \frac{1}{1609.34\times 1609.34}\ mi^2=509.79\ mi^2[/tex]
Each side of the square would be 1320.33 kilometers or 509.79 miles
