Estimating!

[packbat]

Approximating the shape of a tomato as a cube is an example of another general strategy for making order-of-magnitude estimates. A similar situation would occur if you were trying to estimate how many m² of leather could be produced from a herd of ten thousand cattle. There is no point in trying to take into account the shape of the cows' bodies. A reasonable plan of attack might be to consider a spherical cow. Probably a cow has roughly the same surface area as a sphere with a radius of about 1 m, which would be 4π (1 m)². Using the well-known facts that pi equals three, and four times three equals about ten, we can guess that a cow has a surface area of about 10 m², so the herd as a whole might yield 10⁵ m² of leather.

From the Light and Matter series of physics textbooks, Newtonian Physics, Section 1.4 – the textbook alun_clewe plans to use for his class.

I'm only at the beginning, but I must say: so far, very good.