3 ms·
Ah yes, but what interesting, related shape has the volume of 3 times that of a cylinder of a certain base and height, I wonder? Perhaps the coefficient here is
by javajosh 3y ago
Ah yes, but what interesting, related shape has the volume of 3 times that of a cylinder of a certain base and height, I wonder? Perhaps the coefficient here is just coincidentally interesting and there are actually infinitely interesting shapes connected in this manner.
- lisper 3y agoThe general result is that any volume consisting of a stack of cross sections whose area goes does as the square of the distance from the base will have a volume of 1/3 the area of the base times the height. The usual special cases are squares (pyramids) and circles (cones) but it works for any shape. It doesn't even have to be convex.
- lisper 3y ago> whose area goes does as the square of the distance from the base I tried to edit this earlier but apparently it didn't work, and now it's too late. That should read: "whose area goes up as the square of the distance from the tip" but I guess most people were able to figure out what I meant. It's not a particularly difficult concept.