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The volume is defined by a four-step limiting process. First, partition the rectangular region $[a,b] \times [c,d]$ into small subrectangles with area $\Delta A_k = \Delta x_k \Delta y_k$.

Conditions: The base region must be a rectangle $[a,b] \times [c,d]$.; The function $f(x,y)$ defines the height of the surface.; The limit is taken as the largest subrectangle area approaches zero.

The volume is defined by a four-step limiting process. First, partition the rectangular region $[a,b] \times [c,d]$ into small subrectangles with area $\Delta A_k = \Delta x_k \Delta y_k$.

Conditions: The base region must be a rectangle $[a,b] \times [c,d]$.; The function $f(x,y)$ defines the height of the surface.; The limit is taken as the largest subrectangle area approaches zero.