A human liver cell Is approximately spherical with a diameter of 20 mu m. (Show

Question

A human liver cell Is approximately spherical with a diameter of 20 mu m. (Show all calculations for your answers below.) A. Approximately how many of the liver cells could be packed into a cube that is 1 cm on each side (about the size of the tip of your little finger; assume all space in the cube can be occupied by liver cells)? B. A cell membrane is approximately 8 nm wide. How many of these membranes would have to be stacked side-by-side in order to be visible with a light microscope? C. If the human body has a density similar to water (1 g/cm^3), what is the volume (ln m^3) of a 70 kg person? D. If the 70 kg person contains 30 times 10^12 total cells, and each cell is spherical with a diameter of 12.4 mu m, what percentage of the body's volume is occupied by cells? Your hair is composed of proteins known as keratins that have an alpha helix-like fibrous structure. The alpha helix-like structure has approximately 3.6 amino acids per turn of the helix, and a linear dimension of 0.54 nm per turn of the helix. For simplicity, let's imagine that a strand of hair is composed of a single keratin molecule in this alpha helix-like state. If your hair were to grow 25 mm (~1 inch) in one year, how many amino acids must be added to the molecule each minute of the year?

Explanation / Answer

Answer 1A: 23885 cells (As explained below)

1 cm = 103 m

1 cm3 = 109 m3 = volume of 1 cm cube

Volume of one liver cell = (4/3)r3 = (4/3)(3.14)(20/2)3 = (125600/3) = 4186 m3

So, number of cells that can fit into 1 cubic volume = 109 / 4186 = 23885 cells

Answer 1B: 200 (As explained below)

Objects as wide as 0.2m can be viewed by the light microscope.

Width of cell membrane = 8nm = 0.001m = 10-3 m

So, number fo membranes placed side by side that can be viewed by the light microscope = 0.2 / 10-3 = 200.

Answer 1C: 7 x 106 cm3 (As explained below)

Density of water = 1 gm/cc

Volume of 1gm water = 1cm3

Volume of 0.001gm water = 1cm3

Volume of a 70kg person = Volume of 70kg of water = Volume of 70000gm of water = 1cm3 x 70000 gm / 0.001 gm = 7 x 107 cm3 = 7 x 107 x 10-9 m3 = 7 x 10-2m3

Answer 1D: 42.76% (As explained below)

Volume of each cell = (4/3)r3 = (4/3)(3.14)(12.4/2)3 = 997.8m3

Volume of 30 x 1012 cells = 997.8 x 30 x 1012 = 29934 x 1012m3

Volume of 70kg person = 7 x 10-2 m3 = 7 x 10-2 x 1018m3 = 7 x 1016m3

Percentage of body's volume occupied by cells = 29934 x 1012 x 100 / 7 x 1016 = 42.76%

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