Plasma Membrane Calculation Question

Knowing the protein content (number of molecules/ relative concentration) within a plasma membrane can provide information about a cell's function.  Membrane-associated proteins can be easily isolated from plasma membranes and separated by SDS-PAGE.  The proteins are visualized with a dye (Coomassie Blue) whose intensity of color is roughly proportional to the mass of protein present and quantitative estimates can be made as shown in the table below.

Protein            MWn (g/mole)        % of Stain
Melanopsin      275,000                  20.0
Trp 1               125,000                  40.0
Girk 2              20,000                    3.4

a) Using the table above, calculate the number of molecules of Melanopsin, Trp1 and Girk2 in an individual cell.  Assume that 1 ml of cell lysates contain 10^10 cells and 5 mg of total membrane protein.  Show your work.  (Hint: will need to use Avogadro's Number = 6 x 10^23 mol ^-1)

b) What percentage of the plasma membrane (fraction of surface area) is occupied by Trp1.  Assume that the protein is a cylinder 3 nm in radius and 20 nm in height.  The total surface area of a cell is 10^9 nm^2. 

Thank you so much!