number of molecules

[nickname]

If anyone could help me with the following exercise I will greatly appreaciate it!
I had trouble with parts b) and c).

a) if you magnify a cell 10,000 fold, how big will it appear if the the is eukaryotic with a cellular diameter of 50micrometers?

I did 50micrometer= 5.0x10^-5m
5.0x10^-5m times 10,000= 0.5m
0.5m equals 500mm, which is the answer, but how do I solve the following parts?

b) if the cell was a muscle cell, how many actin molecules could it hold, if the cell is spherical and there are no other cellular components present and actin molecules are spherical with a 3.6nm diameter. and the volume of the sphere is 4/3(pi)(r)^3.

I did 3.6nm/2= radius= 1.8nm=1.8x10^-9m
the 50micrometers of the cell equal 5.0x10^-5m

then I did 5.0x10^-5m/1.8x10^-9m= 2.77777777x10^8, but the answer is 2.7x10^12 actin molecules

c) if this were a liver cell of the same dimensions how many mitochondria could it hold? (the cell is also spherical, no other components present and the mitochondria are spherical with a diameter of 1.5micrometers)
The answer is 36,000 mitochodria, but how do I solve it?

 

[Deleted member 4993]

If anyone could help me with the following exercise I will greatly appreaciate it!
I had trouble with parts b) and c).

a) if you magnify a cell 10,000 fold, how big will it appear if the the is eukaryotic with a cellular diameter of 50micrometers?

I did 50micrometer= 5.0x10^-5m
5.0x10^-5m times 10,000= 0.5m
0.5m equals 500mm, which is the answer, but how do I solve the following parts?

b) if the cell was a muscle cell, how many actin molecules could it hold, if the cell is spherical and there are no other cellular components present and actin molecules are spherical with a 3.6nm diameter. and the volume of the sphere is 4/3(pi)(r)^3.

I did 3.6nm/2= radius= 1.8nm=1.8x10^-9m
the 50micrometers of the cell equal 5.0x10^-5m


then I did 5.0x10^-5m/1.8x10^-9m= 2.77777777x10^8, but the answer is 2.7x10^12 actin molecules ..... Where are you using the expression for the volume? It is the ratios of the volume that is needed.

The volume of the actin molecule = 4/3 * (pi) * (1.8)[sup:3mie5ksk]3[/sup:3mie5ksk] * 10[sup:3mie5ksk]-27[/sup:3mie5ksk] m[sup:3mie5ksk]3[/sup:3mie5ksk]

The volume of the muscle cell = 4/3 * (pi) * (25)[sup:3mie5ksk]3[/sup:3mie5ksk] * 10[sup:3mie5ksk]-18[/sup:3mie5ksk] m[sup:3mie5ksk]3[/sup:3mie5ksk]

so # of actin molecule in a muscle cell = (The volume of the muscle cell)/(The volume of the actin molecule) = (25/1.8)[sup:3mie5ksk]3[/sup:3mie5ksk] * 10[sup:3mie5ksk]9[/sup:3mie5ksk] = 2679.183813 * 10[sup:3mie5ksk]9[/sup:3mie5ksk]

c) if this were a liver cell of the same dimensions how many mitochondria could it hold? (the cell is also spherical, no other components present and the mitochondria are spherical with a diameter of 1.5micrometers)
The answer is 36,000 mitochodria, but how do I solve it? .... Same way as above

Find the ratios of the volumes

 

[nickname]

Thank you for replying. For part c) I did:

volume of muscle cell= (4/3)(pi)(25micrometers)^3
volume of mitochondria= (4/3)(pi)(0.75micrometers)^3

same units so I dont have to convert and I ended up with (25/0.75)^3= 37037.03704, but the book says the answer is 36,000 mitochondrias, what steps did I do wrong?

Thank you very much for your help!

 

[nickname]

Oh ok, I rounded wrong 25/0.75=33 and then 33^3=35,937= approximately 36,000 mitochondrias, did I solve this correctly (with the previous part I posted) ?

Thank you