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The volume of a cone can be approximated by carving the cone into slices, and approximating each slice with a cylinder.

To then set it up as a Riemann sum, it helps to orient the cone so that we can sum along the -axis. Mathematica can assist with the visualization:

I don't know why there are grid lines on the slices; they do not appear in Mathematica.

n = 6; (* number of slices *)

```
```h = 20; (* Height of cone *)

r = 15; (* Radius of base of cone *)

deltaX = h/n; (* thickness of each slice *)

`x = 0;`

boxes = List[];

For[i = 0, i < n, i++,
x = x + deltaX;
rAtX = x * r /h ;
boxes =
Append[boxes,
Graphics3D[{Green, Opacity[0.1],
EdgeForm[{Thin, Blue, Opacity[0.1]}],
Cylinder[{{x - deltaX, 0, 0}, {x, 0, 0}}, rAtX]}]]];
Show[boxes, Boxed -> False, Axes -> True, AxesOrigin -> {0, 0, 0},

LabelStyle -> Directive[14]]