Problem with conversion/ order of magnitude

[KublaKhan]

Homework Statement

One cubic centimeter (1.0 cm3) of water has a mass of 1.0 multiplied by 10-3 kg.
(a) Determine the mass of 1.0 m3 of water.

(b) Assuming biological substances are 98% water, estimate the masses of a cell with a diameter of 1.0 µm, a human kidney, and a fly. Take a kidney to be roughly a sphere with a radius of 3.3 cm and a fly to be roughly a cylinder 3.3 mm long and 1.2 mm in diameter. (Type your answer using one of the following formats, 1.2e-3 for 0.0012 and 1.20e+2 for 120.)

Homework Equations

Volume of a sphere - (4/3) * pi * radius^3
Volume of a cylinder - pi * radius^2 * height

The Attempt at a Solution

I believe I am erroneously making the assumption that there should be 100 cubic centimeters in 1 cubic meter. As such, my proposed answer to A was 1.0E-1

It is in fact 1.0E-3
Please clear up this conversion issue for me.

On to the other problems:
I believe if I can get assistance with one, I can figure out the rest.
I have been told to assume 100% water in the calculations of these masses, so never mind the 98%.

Cell Problem: [(4/3)*pi *0.5^3 ] = .5236 *1.0E-3 kg= .005236
So I'm at 5.24E-6 kg for the weight of this cell

The correct answer should be 5.24e-16 kg/cubic centimeter. I am obviously confused over something fundamental. Any help would be much appreciated.

 

[Kurdt]

There are not 100 cubic centimeters in a cubic meter. There are 100 x 100 x 100 cm³ in a cubic meter. Where you're going wrong with the others are with units. You can't just stick a 0.5 in for the radius since your question is giving the diameter of the cell in micrometers.

 

[baba89]

It seems like the main issue here is with the conversion between different units. In order to properly convert between different units, we need to use conversion factors. In this case, we can use the following conversion factors:

1 m = 100 cm
1 cm^3 = 1 mL
1 mL = 1 g

Using these conversion factors, we can solve part (a) of the problem:

(a) 1 m^3 = (100 cm)^3 = 1,000,000 cm^3
1,000,000 cm^3 * 1 mL/1 cm^3 * 1 g/1 mL = 1,000,000 g = 1,000 kg

So the mass of 1 m^3 of water is 1,000 kg.

For part (b), we can use the same conversion factors to convert the given dimensions into cubic centimeters, and then use the density of water (1 g/mL) to find the mass:

Cell: Diameter = 1.0 µm = 1.0E-4 cm
Volume = (4/3) * pi * (0.5 * 1.0E-4)^3 = 5.24E-16 cm^3
Mass = 5.24E-16 cm^3 * 1 mL/1 cm^3 * 1 g/1 mL = 5.24E-16 g = 5.24E-13 kg

Human Kidney: Diameter = 3.3 cm
Volume = (4/3) * pi * (3.3/2)^3 = 14.31 cm^3
Mass = 14.31 cm^3 * 1 mL/1 cm^3 * 1 g/1 mL = 14.31 g

Fly: Length = 3.3 mm = 0.33 cm, Diameter = 1.2 mm = 0.12 cm
Volume = pi * (0.12/2)^2 * 0.33 = 0.00749 cm^3
Mass = 0.00749 cm^3 * 1 mL/1 cm^3 * 1 g/1 mL = 0.00749 g

I hope this helps to clear up any confusion with the conversions and calculations. Remember to always use the appropriate conversion factors and units when solving problems involving different