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Math Help - number of virus particles

  1. #1
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    number of virus particles

    1. The problem statement, all variables and given/known data
    A typical virus is a packet of protein and DNA (or RNA) and can be spherical in shape. The influenza A virus is a spherical virus that has a diameter of 85 nm. If the volume of saliva coughed onto you by your "friend" with the flu is 0.010 cm3 and 1/109 of that volume consists of viral particles, how many influenza viruses have just landed on you?


    2. Relevant equations
    V = 4/3 x pie x r^3


    3. The attempt at a solution
    I'm thinking that I should take half of 85nm which is 42.5nm and plugging it into the volume formula for a spherical. The volume of the whole spherical virus comes out to be 3.21E-5.

    3.21E-5 / 0.010cm^3 = .00321

    1/10^9 of .00321 = 3.11E-7 particles?
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  2. #2
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    Quote Originally Posted by anf9292 View Post
    1. The problem statement, all variables and given/known data
    A typical virus is a packet of protein and DNA (or RNA) and can be spherical in shape. The influenza A virus is a spherical virus that has a diameter of 85 nm. If the volume of saliva coughed onto you by your "friend" with the flu is 0.010 cm3 and 1/109 of that volume consists of viral particles, how many influenza viruses have just landed on you?


    2. Relevant equations
    V = 4/3 x pie x r^3


    3. The attempt at a solution
    I'm thinking that I should take half of 85nm which is 42.5nm and plugging it into the volume formula for a spherical. The volume of the whole spherical virus comes out to be 3.21E-5.

    3.21E-5 / 0.010cm^3 = .00321

    1/10^9 of .00321 = 3.11E-7 particles?
    Hello,

    before you can calculate you have to "harmonize" all metric dimensions:

    0.01 cm = 10^(-8) m

    1/(10^9) = 10^(-9). Therefore the complete volume of all virus-material is: 10^(-9) * 10^(-8) m= 10^(-17) m

    1 nm = 10^(-9) m. Therefore the volume of one spherical virus is according to the given formula: 3.216 * 10^(-22) m.

    The number of virus particals is:
    N=\frac{\text{volume of all}}{\text{volume of one}} =\frac{10^{-17}}{3.216 \cdot 10^{-22}} \approx 31100
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