In general, double integrals calculate volume (or can be interpreted as such).
That is:
[tex]\displaystyle \iint_{A} f(x,t)dA[/tex]
gives the net volume under the function [tex]f(x,y)[/tex] and the x-axis.
However, if [tex]f(x,y)=1[/tex], then the height of the solid is 1 and its volume is equivalent to its base area.
