Volume and surface area
The volume of a 3D shape or solid is how much space it occupies; it is the space contained by the shape. The volume of a container is how much it can hold. This is sometimes referred to as capacity rather than volume.
The volume of the cylindrical paint bucket above is the amount of paint it takes to fill it.
Volume is often measured in cubic units. In the metric system of measurement, cubic measurements include cubic centimeters (cm3), cubic decimeters (dm3), and cubic meters (m3), among others. In the U.S. customary system of units, cubic measurements include cubic inches (in3), cubic feet (ft3), and cubic yards (yd3). When a container is used for holding liquids, its volume may be measured in units of capacity, such as cups, gallons, liters, and so on.
The surface area of a solid is the total area covered by all of its surfaces. One way to think of surface area is as the amount of wrapping paper it would take to exactly wrap the shape.
The surface area of the cylindrical paint can above is the amount of metal it takes to make it (not including the thickness of the metal).
Surface area is measured in square units. In the metric system of measurement, square measurements include square centimeters (cm2), square decimeters (dm2), and square meters (m2), among others. In the U.S. customary system of units, square measurements include square inches (in2), square feet (ft2), and square miles (mi2).