Question

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

Answer 1

Answer:

a

The mass of blood is $m= 5.7876kg$

b

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

Explanation:

From the question we are told that

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

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

         % of blood  that is  cell is  = 45.0%

        % of the blood that is  plasma is  = 55.0%

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

        % of cell that are white is  = 1%

        % of cell that is red is  = 99%

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

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

Generally the mass is mathematically  represented as

               $m = \rho_b * V_b$

Substituting value

            $m = 1060 * 0.00546$

               $m= 5.7876kg$

Mass of cell 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 volume of white blood cell is $V_w$ = 1% of volume of cells

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

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

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

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

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

The number of red blood cell is  $= \frac{V_r}{V_s}$

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

                                                    $= 1.037*10^{13}$

The Number of white blood cell is   $=\frac{V_w}{V_s}$

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

                                                          $= 1.04*10^{11}$

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

                                                        $N_t=1.04*10^{13}$

Answer 2

Answer:

a) The mass of the blood is 5.788 kg

b) The total cells is 1.041x10¹³cells

Explanation:

Given:

V = volume of blood = 5.46 L = 0.00546 m³

ρ = density of blood = 1060 kg/m³

a) The mass of the blood is equal:

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

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

mc = 0.45 * 5.788 = 2.6046 kg

ρc = density of cells = 1125kg/m³

The volume of the cells:

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

Vwc = volume of white blood cells = 1% of volume of the cells

Vwc = 0.01 * 0.0023 = 2.3x10⁻⁵m³

The radius of the cell is:

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

The volume of a single cell is:

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

The number of the red blood cells is:

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

The number of the white blood cells is:

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

The total cells is:

Tc = 1.031x10¹³ + 1.041x10¹¹ = 1.041x10¹³cells