Answer:
n = 1.6*10^9 capillaries
Explanation:
In order to calculate the number of capillaries, you take into account that the following relation must be accomplished:
[tex]A_1v_1=nA_2v_2[/tex] (1)
A1: area of the aorta
v1: speed of the blood in the aorta = 40cm/s
n: number of capillaries = ?
A2: area of each capillary
v2: speed of the blood in each capillary
For the calculation of A1 and A2 you use the formula for the cross sectional area of a cylinder, that is, the area of a circle:
[tex]A=\pi r^2\\\\A_1=\pi r_1^2=\pi(1.0cm)^2=3.1415 cm^2\\\\A_2=\pi r_2^2=\pi (5*10^{-4}cm)^2=7.85*10^{-7}cm^2[/tex]
Where you have used the values of the radius for the aorta and the capillaries.
Next, you solve the equation (1) for n, and replace the values of all parameters:
[tex]n=\frac{A_1v_1}{A_2v_2}=\frac{(3.1415cm^2)(40cm/s)}{(7.85*10^{-7}cm^2)(0.10cm/s)}=1.6*10^9[/tex]
Then, the number of capillaries is 1.6*10^9
