8 comentarios en “caltulations”

  1. I don’t really see why Sophie needs to know about the intersection of two circles in 2-dimensional Cartesian space (which is what it looks like she’s trying to calculate)…

    I would think that the main thing she’d be trying to work out would be the approximate volume of a 3-dimensional cylinder, possibly with the addition of a hemispherical end-cap (at least to a first order approximation).

    If the length of the cylinder is D, and it has a radius R, then the volume (V) of the object would be the sum of the cylinder’s and hemispherical end-cap’s volumes, e.g.,

    V(Artur) = πD(R^2) + (1/2)(4/3)π(R^3) = π(R^2)(D +(2/3)R),

    (where “^” symbol means “raise to the power of”, since I don’t believe one can insert proper squared and cubed symbols into the text comments on Deviantart… I just hope the “pi” symbol (“π”) comes through on most web browsers!)

    But then… in this context, I don’t think a total volume metric would really tell you much of anything you’d really want to know.

    I rather think that the quantity that Sophie would more likely be interested in determining would be the cylinder+end cap net SURFACE AREA (A), which would be:

    A(Artur) = 2πRD + (1/2)(4πR^2) = 2πR(D + R).

    Yeah, upon further consideration the surface area would definitely be the metric of interest to Sophie, because this could more easily be related to a net force vector on the object, assuming that one knew the surface coefficient of dynamic friction…

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