Solids
A box, a can and a ball all take up room. How do you describe a solid, unfold it, slice it and measure what it covers and holds?
Where you are 8 inside
What this area is about
A solid is a shape in three dimensions. This area names solids and their parts, then measures them: a net for the outside, a slice for the inside, coordinates for position, and formulas for surface area and volume.
How these fit together
Naming. Three-dimensional shapes covers faces, edges and vertices, polyhedra, prisms and pyramids, cylinders, cones and spheres, and the five regular solids.
Position. Coordinates in space pins a point with three numbers (x, y, z) and measures the distance between two points.
Flattening. Nets unfold a prism, pyramid or cylinder into one flat piece. Cross sections name the flat shape a plane cut leaves. Solids of revolution describe a round solid by the flat region spun about a line to make it.
Measuring. Surface area totals the outside: the face areas, a curved side unrolled flat, or for a sphere a formula of its own. Volume stacks copies of a base, then finds a pyramid, cone or sphere as a fraction of a matching prism or cylinder.
Using it. Modeling with solids treats real objects as solids to judge weight, material and design.
A path through it
Three-dimensional shapes first, except that its five regular solids wait until after coordinates in space, which they use. Then nets before surface area, and cross sections before volume. Solids of revolution uses the volume formulas and is cited by cross sections, so read it beside those two. Modeling with solids comes last: it needs surface area and volume.
This area leads to the double cone and, in calculus, volumes with known cross sections.