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?

Note that you might need to use standard scientific data not provided in the questions for some of the numbers used and you might need to use a calculator. You will certainly need to decide which formulas to use to relate the quantities in the question.

1.) I have a set of ball bearings of volume 1cm3. 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 850cm3.

It’s an under estimate. We need more information of how they’re packed, and the size of the box.

2.) In a wood of area 27,000m2 I find 17 earthworms in a volume of soil of 1m2 in area and 20 cm deep. I therefore estimate that there are 459,000 earthworms in the wood.

Estimate is a little low. We need to know what kind of earth worms, and how deep do earthworms dig.