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# Assume for this question that biological tissue is 100% water.

### Resolved Question:

Assume for this question that biological tissue is 100% water. Given that the density of water is
roughly 103 kg/m3 estimate the mass of (a) a human cell of diameter 1 μm = 10−6 m and (b) a
honey bee.
Submitted: 2 years ago.
Category: Homework
Expert:  Ray Atkinson replied 2 years ago.

Ray Atkinson :

Are you given the volume of a honeybee?

JACUSTOMER-uyfuw5na- :

1cm

Ray Atkinson :

Ok, thank you. I will get this written up right away.

JACUSTOMER-uyfuw5na- :

thanks

Ray Atkinson :

That is the diameter of the bee, correct?

Ray Atkinson :

or is it 1 cm³?

JACUSTOMER-uyfuw5na- :

he was not precise i think it was the size

Ray Atkinson :

Actually, since (1 cm)³ = 1 cm³, it does not matter.

Ray Atkinson :

The formula for volume from a diameter is 4/3*π*(d/2)³, so the human cell is 4/3*π*(5 * 10^(-7))³ = 5.23598776 * 10^-19 m³

Ray Atkinson :

forgive me, but i am having tech problems tonight. Computer keeps freeziong on me.

JACUSTOMER-uyfuw5na- :

sorry but where did you get 4/3? i was using formula density = m/v

Ray Atkinson :

Going from diameter to volume of a sphere is 4/3*π*r³

Ray Atkinson :

and r = d/2

JACUSTOMER-uyfuw5na- :

he said we do not have to use the radius he wants the density

Ray Atkinson :

You need the volume before you can use the density formula.

Ray Atkinson :

The question is to find the mass. You are given water as mass/volume. You need to get the volume to solve.

JACUSTOMER-uyfuw5na- :

sorry is this for the bee or cell

Ray Atkinson :

The mass of the cell is 5.23598776 * 10^-19 m³ * 103 kg/m³ =NNN-NN-NNNN* 10^-19 kg = 5.39306739 * 10^-17 kg

JACUSTOMER-uyfuw5na- :

could you explain via a formula d=v/m please

Ray Atkinson :

Sorry, frozen again. Be patient with me.

JACUSTOMER-uyfuw5na- :

no problem

Ray Atkinson :

Sure. density is mass over volume. 103 = m / 5.23598776 * 10^-19

Solve for m by multiplying both sides by 5.23598776 * 10^-19 to get m = 5.39306739 * 10^-17

Ray Atkinson :

I am going to assume the 1 cm for the honeybee is the diameter, since you were given the diameter for the other problem.

Ray Atkinson :

[Is this showing on your side?]

Ray Atkinson :

v = 4/3 * π * (0.005 m)³ = 4/3 * π * 1.25 * 10^-7

d = m/v, so 103 kg/m³ = m / 1.25 * 10^-7 m³

Multiply both sides to 1.25 * 10^-7 to get

1.2875 * 10^-5 kg

JACUSTOMER-uyfuw5na- :

ok

Ray Atkinson :

Does that all make sense? If not, I can write it up in a word file with all the units lined up for you.

JACUSTOMER-uyfuw5na- :

whats the unit for the 5.23 ans

Ray Atkinson :

kilograms. That is the unit that is given by your instructor for the mass of water.

Ray Atkinson :

It is also the standard form of mass units.

JACUSTOMER-uyfuw5na- :

could you write up a word file cause i am lost

Ray Atkinson :

Certainly. How fast do you need it?

Ray Atkinson :

Ray Atkinson :

(I'm never sure with daylight savings time)

JACUSTOMER-uyfuw5na- :

its 2am

JACUSTOMER-uyfuw5na- :

like asap

Ray Atkinson :

All right. I'll get on it. Will have it all doen within a half hour. Will work?

Ray Atkinson :

plus I need to seriously reboot this computer.

JACUSTOMER-uyfuw5na- :

ok i will be waiting

Ray Atkinson :

Ok, I'm on it. I'll be back as soon as I can.

JACUSTOMER-uyfuw5na- :

i am confused the diameter of the cell is 10cubes

JACUSTOMER-uyfuw5na- :

how do you superscript in this chat

Ray Atkinson :

hold down <alt> and type 253 to get ², and type 0179 to get ³

Ray Atkinson :

If the diameter is 1 cm, then the radius is 0.5 cm. The volume is 4/3 * π * (0.5 cm)³

Ray Atkinson :

0.5 cm = 0.005 m = 5 · 10^-3 m

(5 · 10^-3 m)³ = 125 * 10^-9 m

JACUSTOMER-uyfuw5na- :

no the diameter of the cell is 10^-6m

Ray Atkinson :

Oh, I get it. That is 10 to the -6 power. 0.000001 m

Ray Atkinson :

Half that is 0.0000005 m is the radis

JACUSTOMER-uyfuw5na- :

yes

Ray Atkinson :

= 5 · 10^-7

JACUSTOMER-uyfuw5na- :

can you please give me both ans explained so i can finish my revision question

Ray Atkinson :

I am typing right now

JACUSTOMER-uyfuw5na- :

thanks

Ray Atkinson :

 Full Size Image

See if you can read this.

Ray Atkinson :

The numbers look very similar, since the diameters are 5*10^-7 m and5*10^-3 m

Ray Atkinson :

JACUSTOMER-uyfuw5na- :

thanks got quest 1 but where do you get (5x10^7)??

JACUSTOMER-uyfuw5na- :

in you ans in word you sent me its after phi

Ray Atkinson :

phi?

Ray Atkinson :

oh pi

JACUSTOMER-uyfuw5na- :

yes

Ray Atkinson :

For some reason, the last cople things you typed are not showing. I am going to switch this to Q&A format rather than chat, so I can see everything.

Category: Homework
Satisfied Customers: 1796
Experience: Inner-city high school substitute teacher. Degrees in mathemetics, accounting, and education. Years and years of tutoring.
Expert:  Ray Atkinson replied 2 years ago.
Since the diameter is 1·10^6, the radius is half that, so is 0.5·10^-6 = 5·10^-7
Expert:  Ray Atkinson replied 2 years ago.
Is everything else there clear?
Customer: replied 2 years ago.
The accept button is not working how do I give you credit
Customer: replied 2 years ago.
,
Expert:  Ray Atkinson replied 2 years ago.

Expert:  Ray Atkinson replied 2 years ago.
My chat with you is marked as the answer. If that did not set it, then this one will.
Expert:  Ray Atkinson replied 2 years ago.

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