Physics question

well saying that the radiation from the sun all travels at the same speed
, this radiation will cover a spherical shape of area.(just like blowing a balloon)

now the distance of the earth to the sun is about $1.5x10^{11}m$
this means you need to find the surface area of a sphere with a radius of $1.5x10^{11}m$ , then you need to find the area of intersection between the sphere and the earth(assume to be in the middle of the earth)

surface area of the sphere:
$<br /> A_1 = 4\pi r_{ES}^2<br />$
where $r_{ES} ^2$ is the radius of the earth and has the value of $1.5x10^{11}$

hence the area of intersection is:
$<br /> A_2 = \pi r _E ^2<br />$

where $r_E ^2$ is the radius of the earth and has the value of $6.4x10^6$ . The area of intersection is can be assumed as a circle since the distance of the earth from the sun is very much larger tahn the radius of the earth.

hence the fraction of radiation received by earth is
$\frac{A_2}{A_1}$