Volume and capacity
How much space does a solid take up, how much liquid does a container hold, and how do you find either without filling it?
Where you are 9 inside
What this area is about
Volume is how much space a solid takes up; capacity is how much a container holds. Liquid is measured by filling a unit container, such as a liter, and a solid by packing it with unit cubes. For a box, packing becomes a formula: three edge lengths give the volume.
How these fit together
Liquid amounts. Volume does not change when it is poured shows that water in a taller glass is not more water. Liters and milliliters and cups, pints, quarts and gallons are the units.
Volume of solids. Volume as filling defines volume by counting unit cubes. Volume with unit cubes counts them in layers, and the volume of a box turns that into length times width times height, V = lwh.
Extending the formula. Fraction edge lengths shows V = lwh still holds when the edges are fractions. Solids made of boxes split a shape into boxes and add, or subtract a hollow part.
A different measure. Surface area covers the outside of a solid, and two boxes with the same volume can need different amounts of it.
A path through it
Pouring needs only comparing two objects, so it can come first. Then liters and milliliters, then customary units and volume as filling. Unit cubes follow, also needing the area of a rectangle, then the box formula. Fraction edges, composite solids and surface area all come after it.
Next: density, flow rate and converting cubic units.