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3 months ago

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Jeff's body contains about 5.46 L of blood that has a density of 1060 kg/m3. Approximately 45.0% (by mass) of the blood is cells

and the rest is plasma. The density of blood cells is approximately 1125 kg/m3, and about 1% of the cells are white blood cells, the rest being red blood cells. The red blood cells are about 7.50????m across (modeled as spheres).
a. What is the mass of the blood mblood in Jeff's body?

mblood=________________________kg

b. Approximately how many blood cells (of both types) ????N are in Jeff's blood?

????= _______________ blood cells

2 answers:

ValentinkaMS [3.4K]3 months ago

6 0

Answer:

a) Blood mass is $m= 5.7876kg$

b) The count of blood cells is $N_t=1.04*10^{13}$

Explanation:

From the problem statement, we learn that

The blood volume is $V_b = 5.46 \ L = \frac{5.46}{1000} = 0.00546m^3$

The density of blood is $\rho_b = 1060 kg/m^3$

% of blood which consists of cells is = 45.0%

the % of blood that is plasma is = 55.0%

density of blood cells is $\rho_d = 1125kg/m^3$

% of cells that are white is = 1%

% of cells that are red is = 99%

The red blood cell diameter is = $7.5 \mu m = 7.5*10^{-6}m$

The red blood cell radius is $= \frac{7.5*10^{-6}}{2} = 3.75*10^{-6}m$

The mass is generally represented mathematically as

$m = \rho_b * V_b$

Substituting values

$m = 1060 * 0.00546$

$m= 5.7876kg$

Cell mass is $m_c$ = 45% of m

= 0.45 * 5,7876

= 2.60442 kg

The volume of cells is $V_c$ = $\frac{m_c}{\rho_d}$

$= \frac{2.60442}{1125}$

$= 2.315 *10^{-3} m^3$

The white blood cells volume is $V_w$ = 1% of the cells volume

$= \frac{1}{100} * 2.315*10^{-3}$

$= 2.315*10^{-5}m^3$

The volume of a single cell is $V_s = 4 \pi r^3$

$= 4*(3.142) * (3.75*10^{-6})^3$

$= 2.21*10^{-16}m^3$

The red blood cells volume is $V_r = V_c - V_w$

$=2.315*10^{-3} - 2.315*10^{-5}$

$= 2.29*10^{-3}m^3$

The total red blood cell count is $= \frac{V_r}{V_s}$

$= \frac{2.29 *10^{-3}}{2.21*10^{-16}}$

$= 1.037*10^{13}$

The total white blood cell count is $=\frac{V_w}{V_s}$

$= \frac{2.315 * 10^{-5}}{2.21*10^{-16}}$

$= 1.04*10^{11}$

The overall number of blood cells is $N_t= 1.037*10^{13} + 1.04*10^{11}$

$N_t=1.04*10^{13}$

Softa [3K]3 months ago

6 0

Answer:

a) The blood mass is 5.788 kg

b) The total blood cells are 1.041x10¹³cells

Explanation:

Given data:

V = blood volume = 5.46 L = 0.00546 m³

ρ = blood density = 1060 kg/m³

a) The mass of the blood is given by:

$\rho =\frac{m}{V} \\m=\rho V=1060*0.00546=5.788kg$

b) mc = mass of cells equals to 45% of blood mass

mc = 0.45 * 5.788 = 2.6046 kg

ρc = cells density = 1125kg/m³

Cell volume:

$V_{c} =\frac{m_{c} }{\rho _{c} } =\frac{2.6046}{1125} =0.0023m^{3}$

Vwc = white blood cell volume = 1% of total cells volume

Vwc = 0.01 * 0.0023 = 2.3x10⁻⁵m³

The radius of a cell is:

$r_{c} =\frac{7.5x10^{-6} }{2} =3.75x10^{-6} m$

The volume of one cell is:

$V_{sc} =\frac{4\pi r^{3} }{3} =\frac{4\pi (3.75x10^{-6})^{3} }{3} =2.209x10^{-16} m^{3}$

The red blood cell count is:

$N_{rc} =\frac{0.0023-2.3x10^{-5} }{2.209x10^{-16} } =1.031x10^{13} cells$

The white blood cell count is:

$N_{wc} =\frac{2.3x10^{-5} }{2.209x10^{-16} } =1.041x10^{11} cells$

The total cell count is:

Tc = 1.031x10¹³ + 1.041x10¹¹ = 1.041x10¹³cells

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