One cubic foot
The number of cubic feet (or inches, or yards) in the volume of a rectangular solid is equal to the number of linear feet (or inches, or yards) in the length, multiplied by the number of linear feet (or inches, or yards) in the breadth, multiplied by the number of linear feet (or inches, or yards) in the thickness.
This is usually abbreviated into
Length × breadth × thickness = volume, or cubic content.
For example, suppose the solid in the [diagram] is 10 feet in length, 8 feet in breadth, and 5 feet in thickness. It is clear that the solid can be cut into five slices, each 1 foot thick, by planes parallel to the bottom. But, the bottom contains 10×8 square feet and above each square foot there is a cubic foot. Thus, each slice contains 10×8 cubic feet. Therefore, since there are five slices, the whole solid contains 10×8×5, or 400 cubic feet.
Since length × breadth × thickness = cubic content, it follows that, if we know any three of these four quantities, we can find the fourth.
The student should remember that
(a) A cubic foot of water weighs 1000 ounces (avoirdupois) approximately.
(b) A gallon of pure water weighs 10 pounds (avoirdupois).
We have thus a relation between weight, capacity, and cubic content.