Use linear approximation to estimate the amount of paint in cubic cms needed to apply a coat of paint 0.030000 cm thick to a hemispherical dome with a diameter of 50.000meters?

The area of a hemisphere is
  area = 2*pi*r^2 = (pi/2)*d^2
Your hemisphere has an area of
  area = (pi/2)*(5000 cm)^2
  = pi*1.25*10^7 cm^2
The volume of paint can be approximated by multiplying this area by the thickness of the paint.
  Volume = area*thickness
  = (pi*1.25*10^7 cm^2)*(3*10^-2 cm)
  = pi*3.75*10^5 cm^3
  = 1,178,100 cm^3    (rounded to 5 significant digits)