Imagine dividing the first quadrant of the xy-plane, under the cone into small regions. The area of each region is

. Now imagine extending each region up to the cone. It has height z and so volume

. The volume you want would be, approximately, the sum of those volumes over all the regions. That is, of course, a "Riemann sum" and, in the limit as the size of the regions goes to 0, you get the volume equal to the integral

.

Since you have given the equation of the cone in terms of "r": z= 1- r rather than

, I presume you want to use polar coordinates. To cover the entire base of the cone, obviously, r must go from 0 to 1 and to get the entire first quadrant,

must go from 0 to

. Don't forget that the "differential of area" in polar coordinates is

.

The volume is given by

.