# Math Help - number of virus particles

1. ## 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?

2. Originally Posted by anf9292
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 cm³ = 10^(-8) m³

1/(10^9) = 10^(-9). Therefore the complete volume of all virus-material is: 10^(-9) * 10^(-8) m³= 10^(-17) m³

1 nm = 10^(-9) m. Therefore the volume of one spherical virus is according to the given formula: 3.216 * 10^(-22) m³.

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