Problem: Find the volume of a regular cone whose height is h and the radius of its circular base is r.
Solution: The key to a successful solution here is a proper placement of the cone:
Now we see that the cone is equal to the solid obtained by revolving (about
the x-axis) the region under the graph of
We can also try the method of cross-sections. When we slice the cone parallel to the base at a position x, the cross-section is a disc.
The radius of the cross-section can be found using similarity of triangles:
Thus we get the area of a cross-section:
Now we can apply the formula from the section More on volume:
