Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity I is
I=\frac{P}{A}
Where P is the power through an area A.
Rearranging to find the Power we have that,
P = IA
The value of the given area for land can be approximated to that of a sphere, therefore the Area would be equivalent to
[tex]A = 4\pi r^2[/tex]
Where r represents the distance from the sun to the earth.
Replacing with our values we have that
[tex]P = (1350W/m^2)(4\pi r^2)[/tex]
[tex]P =1350*(4\pi (1.5*10^{11})^2)[/tex]
[tex]P = 38151*10^{22} W[/tex]
Therefore the average power output of the sun is [tex]P = 38151*10^{22} W[/tex]
