Assume the sun is a sphere (it’s not exactly, but close enough for a good estimate). The surface area of a sphere is [math]A=4 \pi r^2[/math] Putting in the radius of the sun r=696300 km, [math]A=4 \pi \left ( 696,300 \right )^2[/math] A = 6,092,599,834,867 square km. About 6 trillion square kilometers. read more