Volumes of solids with known cross sections calculator

The solid shown in Figure is an example of a cylinder with a noncircular base. To calculate the volume of a cylinder, then, we simply multiply the area of the cross-section by the height of the cylinder: V=A⋅h. In the case of a right circular cylinder (soup can), this becomes V=πr2h.

The height of each triangular cross-section is twice the length of the base and the cross-sections are perpendicular to the x-axis. V=∫baA(x) dx V = ∫ a b A ( x ) d x .

The volume by cross section method takes the area of all of the slices of the shape and adds them together to find the total volume. For two shapes, if the corresponding slices have the same area then the sum will be the same and the shapes will have the same volume.