Finding the Volume of a Solid with Congruent Cross Sections
Knowing how volume is measured without calculus pays off bigtime when you step into the calculus arena. This is strictly nobrainer stuff — some basic, solid geometry that you probably know already.
One of the simplest solids to find the volume of is a prism. A prism is a solid that has all congruent cross sections in the shape of a polygon. That is, no matter how you slice a prism parallel to its base, its cross section is the same shape and area as the base itself.
The formula for the volume of a prism is simply the area of the base times the height:
V = A_{b} · h
So if you have a triangular prism with a height of 3 inches and a base area of 2 square inches, its volume is 6 cubic inches.
This formula also works for cylinders — which are sort of prisms with a circular base — and generally any solid that has congruent cross sections. For example, the oddlooking solid in the figure fits the bill nicely. In this case, you’re given the information that the area of the base is 7 cm^{2} and the height is 4 cm, so the volume of this solid is 28 cm^{3}.
Finding the volume of a solid with congruent cross sections is always simple as long as you know two things:

The area of the base — that is, the area of any cross section

The height of the solid