Suppose I want to make a snowman out of a bunch of spherical balls of snow and I want him to be tall, with a bunch of balls stacked on top of the other, the one on top infinitesimally smaller than the last decreasing.

Question

kainui · Answer

Now if I were to integrate the formula for a sphere:

$$\int\limits_{0}^{ height}4\pi /3r^3dr$$ does that equal the volume of the infinite number of snowballs stacked up on top of each other?

agent0smith · Answer

Hmm. Is this what you mean by the decreasing snowballs? |dw:1355407062743:dw|

kainui · Answer

Exactly what I mean. I'm basically envisioning the disk method, but with spheres lined up

agent0smith · Answer

I wrote an answer earlier but then the site refreshed and erased it. I don't think your integral for the volume is correct but I'm not 100% sure. 

I was comparing it to the disk method too, but in the disk method, dr is the thickness of the disks - here, dr is the decrease in radius from one sphere to the next. And the height would be given by the sum of the diameters of the spheres (or 2 times the sum of radii).