# Integration of a cone to find centre of mass

1. Oct 14, 2004

### rainbowGirl

Can anyone help me with this question?

A uniform solid cone of height b and base radius a stands on a horizontal table. Find an expression for the volume of the disc at height h above the base. Integrate over all the discs to show that the total volume, V, is given by V =pi/3 * b * a^2

2. Oct 14, 2004

### HallsofIvy

Start by drawing a picture. Seen from the side, the cone looks like a triangle with base 2r and height b. Now draw a line across the triangle at height h (and so b-h from the vertex). Use "similar triangles" to find the base of that triangle, as a function of h. The disk formed by the cone has that base as diameter and thickness dx. I assume you know that the voume of a disk of diameter d and thickness s is pi(d2/4)s.