🚀 go-pugleaf

On Sat, 26 Jan 2008 15:03:21 -0500, "Greg Neill"
<gneillREM@OVEsympatico.ca> wrote:

>"Jolt Joltist" <joltist@hotmail.com> wrote in message
>news:3p1np3p789fcukd0ssd3ssiip1vtp8k7se@4ax.com...
>> I need help with some homework.
>>
>> Cells can be 2.0 um in diameter and cell wall 50.0 nm thick.  If
>> density(mass divided by volume) of the wall material is the same as
>> that of water,  what is the mass in mg of the cell wall, assuming the
>> cell to be spherical and the wall to be a thin spherical shell?
>>
>> How do you work this out?
>>
>>
>> I tried subtracting the volume of a sphere without the cell wall from
>> a sphere with the cell wall to get the cell wall.
>
>Good approach.
>
>>
>> outer radius is 2.0 um/2  = 1.0 um.  volume is 4/3(pie)r * r * r =
>> 3.351 * 10^-17.   I have trouble here converting units.   I don't know
>> what unit this answer is or how to get it to a useful unit.
>
>(4/3)*pi = 4.189
>
>(1.0 um)^3 = 1.0 um^3    [one cubic micrometer]
>
>So the volume of the cell is
>
>4.189 um^3
>
>>
>> inner radius is (2.0 um/2) - 50.0 nm = 1.95 * 10^-6.  Is that right?
>> Again, what units are we in here?  Anyway, this sphere has volume
>> 4/3(pie)r^3 = 3.1059 * 10^-17.
>
>50 nm = 0.050 um
>
>1.0 um - 0.050 um = 0.95 um
>
>(4/3)*pi*(0.95um)^3 = 4.189*(0.95)^3 * (um)^3
>                    = 4.189*0.857 um^3
>                    = 3.591 um^3
>
>>
>> Subtracting sphere 2 from sphere 1     (3.351 *10^-17) - 3.1059 *
>> 10^-17 = 2.4506 * 10^-18, volume of the cell wall.   I hope.
>
>v = 4.189 um^3 - 3.591 um^3 = 0.597 um^3
>
>>
>> I'm lost at this point, what units is this in?  How do I get to the
>> mass in mg?
>
>So far I've left the units in cubic micrometers.
>You have a choice now to convert to cubic centimeters and use the
>density of water in grams per cubic centimeter, or convert the
>density to terms of cubic micrometers.  Let's do the latter.
>
>Density of water: 1.0 g/cm^3
>
>      gm    1000 mg      (cm)^3
>1.0* ---- x ------- x ------------ = 1.0 x 10^-9 mg/um^3
>     cm^3     g       (10,000um)^3
>
>Multiply the calculated volume by the density to arrive at the
>mass in mg:
>
>0.597 um^3 * 1.0x10^-9 mg/um^3 = 6.0 x 10^-10 mg
>rounded to one decimal place to match the given
>precision.
>
>