pancreatic β-cell calculation - (Nov/29/2006 )

I don't know how to answer this question.. can anyone help?


A pancreatic β-cell that is cuboidal in shape (10 μm unit length) produces 1 million molecules of
insulin (molecular weight = 5600 daltons) that are stored in dense core secretory granules, each
approximately 300 nm in diameter. Calculate the following:

I) If the insulin-containing granules occupy 10% of the cell volume, how many granules are present
in each cell ?

II) After an extensive chocolate binge, if a quarter of the insulin-containing vesicles fuse with the
plasma membrane releasing their contents, what is the percentage change in surface area for a cell?

III) What is the molar concentration of insulin in each secretory granule?

q2: enlargement of secretory membrane may be given during secretion but I suppose that n parallel endocytosis is working; so, one has to estimate dynamics of exocytosis as well as of endocytosis to calculate the relative enlargement of the apical membrane

volume of granules = 4/3 x pi x r x r x r (means r^3)
volume of a cell = 10 x 10 x 10 µm^3
so the rest is easy

surface of sphere = 4 x pi x r² so the increase of cell surface is pi x (r of granule)²

question 3 : just units changes aand few calculation are needed.