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A set of estimates of various physical quantities is shown below. For each estimate, consider the following three questions:

• Do you think that the estimation will be an over- or under-estimate, or will it be essentially exactly correct? Or will it be impossible to say without more information? Be as clear as you can with your reasoning.
• Why do you think that the solver made the estimate in this way? What assumptions were made? Can you reproduce the calculation?
• How close do you think the estimations would be to the real values?

1. I wish to estimate the volume of an apple. It weighs 76.2g. I therefore estimate its volume to be 76.2cm$^3$.
    
2. I have a set of ball bearings of volume 1cm$^3$. A large crate is filled to the brim with ball bearings and closed with a lid. The box contains 850 ball bearings, so I estimate that the box has a volume of 850cm$^3$.
    
3. An oak tree measures 106cm around the base, corresponding to a cross section of 0.0894m$^2$. I have measured the height to be 7.3m. I estimate the volume to be 0.65m$^3$. How would your answer differ if the question related to a fir tree (with the same numbers)?
    
4. In a wood of area 27000m$^2$ I find 17 earthworms in a volume of soil of 1m$^2$ in area and 20 cm deep. I therefore estimate that there are 459000 earthworms in the wood.
    
5. A cheetah can run at 100km h$^{-1}$, so in a 3 minute chase of prey I estimate that it might be able to run 5km.
    
6. A 10 kg sample of sea water taken from a point far from the shore contains 350g of salts. Therefore, to obtain 100kg of salts I would need to take a sample of 3000kg of sea water.
    
7. A cylindrical container barrel has a capacity of 700l. To obtain the 100kg of salts required in question 6, I would only need to fill 4 barrels.
    
8. A bacterial culture initially contained 7 cells. After 35 minutes it contained 14 cells and after 1 hour 10 minutes it contained 28 cells. I estimate that after a further 12 hours there will be around 43.6 million cells.
    
9. I catch 100 adult fish from a lake and mark them all with a tag. One week later I catch 100 adult fish from the lake and find that 12 of them are marked. I estimate that there are 800 adult fish in the lake.
    
10. Light of a certain wavelength is shone through a solution of plant cells. 90% of this light is absorbed by the solution. If this solution was diluted 1 part solution to 9 parts water then I estimate that 10% of the same light would be absorbed. A second solution absorbs 100% of this light. I estimate that a 10% dilution would absorb 10% of the light.