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.,

(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…

Little does she know that Arthur is also very interested in math AND physics… particularly in the area of mass, buoyancy, elasticity, circumference, displacement volume, not to mention kinetic energy, fluid capacity, speed, acceleration, velocity, time… etc etc…

hahaha

She be like:

“It’s gonna be in me someday”

Author is actually quite well hunged eh?

She’s got a good grip on the… numbers, alright.

At least she’s boning up on her English.

*Calculations, or Calculus. (not sure which you were going for in the title)

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…

NEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEERD xD

Little does she know that Arthur is also very interested in math AND physics… particularly in the area of mass, buoyancy, elasticity, circumference, displacement volume, not to mention kinetic energy, fluid capacity, speed, acceleration, velocity, time… etc etc…

…Followed closely by biology.