Volume of Solids

Core concept

A useful relationship to remember is that a cone's volume is always exactly one-third of a cylinder's volume when both share the same base radius and height — this can even be demonstrated experimentally by filling a cone-shaped container with water or sand and pouring it into a same-sized cylinder exactly three times to fill it. These volume formulas are essential for practical calculations, from determining how much liquid a container can hold to calculating the amount of concrete needed for construction.