One cubic centimeter (1.0 cm3) of water has a mass of 1.0 10-3 kg. Assuming biological substances are 98% water, estimate the mass of a (spherical) cell with a diameter of 1.0 µm.

Question

One cubic centimeter (1.0 cm3) of water has a mass of 1.0  10-3 kg.  Assuming biological substances are 98% water, estimate the mass of a (spherical) cell with a diameter of 1.0 µm.

mrnood · Answer

It says estimate - and gives oyu 98% water content. In this case I would assume that the cell is essentially a sphere of water.

The volume of a sphere is 4(pi r^3)/3
mass = density * volume
1 mu (micron) is 10^-3mm

mrnood · Answer

Also - note
Be very careful about units and exponents. (remember to cube a number you multiply the exponent by 3)
The density is referenced to cm, but the diameter is micron
The volume of this drop is going to be a minute fraction of a cm^3

anonymous · Answer

You could check another way by temporarily assuming a cube of side 1um = 10^-6 m  Which gives you 10^-18 m^3 volume, slightly more than the sphere. Density of water is 1000 kg/m3.

mrnood · Answer

A sphere sits inside a cube of side 2r
So the cube has volume (2r)^3 = 8r^3
4*pi/3 is approx. 4 = so the cube has nearly twice the volume of the sphere - in my mind not a good approximation given the other info in the question.