If an egg were a perfect sphere, then finding its volume would be easy: just measure the radius r and use the formula you learned way back in grade school, V = (4/3)πr³ (why that formula works is another story for another day). But, alas, eggs are not spheres, but, well, egg-shaped. So what can we do?
Eggs aren’t even elliptical, but they are well-approximated by a pair of ellipses. That is, if we take a cross-section then we can realize it as in this diagram:
Now we can use calculus to get the volume. The egg is obtained by revolving this shape around the x-axis and the volume is given by
So now you can figure out just how much creme there is in your filled chocolate egg. I’ll leave it as an exercise to compute the surface area so you’ll know how much chocolate you’re eating.
Scritto da Kevin Knudson