posted by Jack .
Calculate the volume of the ramp in Figure 17 in three ways by integrating the area of the cross sections:
(a) Perpendicular to the x-axis (rectangles)
(b) Perpendicular to the y-axis (triangles)
(c) Perpendicular to the z-axis (rectangles)
We do not see the figure, but could probably help anyway.
Along whichever axis you do the integration, the method is to cut up the volume into slices perpendicular to the x-axis, say. Each slice is of thickness dx and the width and height will be a function of y and z, which should in turn be transformed to a function of x. Do the integration along the x-axis and find the volume.
You can proceed in a similar way along the two other axes. The resulting volumes should, of course, be identical.