How is the total volume of blood in the arterioles calculated?
Since you already know the total volume I presume you wish to know how to arrive at the figure from the given dimensions. These arterioles are tiny cylinders (like a miniature tin of beans, for example.) The volume of a cylinder is given by the formula π r² h ( r = radius of cylinder, h = height, or length of cylinder) The diameter = 0.002 cm, or 2 x 10^-3 Length = 0.2 cm, or 2 x 10^-1 (The standard scientific notation is the best way of keeping track of the zero’s in calculations like this) So, cross-section area of one arteriole = π x (10^-3)² = π x 10^-6 Number of arterioles = 4 x 10^7, so total cross-sectional area = π x 10^-6 x 4 x 10^7 which = π x 4 x 10¹ or, in other words, = 40π, which works out as 125.66 cm² Now you just have to multiply by the length of the cylinder to find the volume : Volume = 40π x 2 x 10^-1 = 8π, which works out as 25.1 cm². Hope that is what you required.
