Stereometry: lines and planes in space, polyhedra, solids of revolution, areas and volumes
Space: lines, planes, solids
In space, two lines may be parallel, intersecting, or skew (neither parallel nor intersecting, non-coplanar). A line is perpendicular to a plane if it is perpendicular to two intersecting lines of that plane. The theorem of three perpendiculars converts a spatial right angle into a planar one - the standard tool for dihedral angles and distances from a point to a plane.
Polyhedra: prism V = S_base·h; pyramid V = ⅓S_base·h. Worth memorising: the cube's space diagonal is a√3.
Solids of revolution: cylinder V = πr²h, lateral area 2πrh; cone V = ⅓πr²h, lateral area πrl with slant height l = √(r² + h²); sphere V = (4/3)πr³, surface 4πr².
Scaling: multiply all lengths by k → areas multiply by k², volumes by k³.
Traps. Using the height instead of the slant height in a cone's lateral area (or the reverse). Omitting the base from total surface area, or counting it twice. Mixing radius and diameter. Assuming a pyramid's apex projects to the centre of its base unless the problem says so.
Worked example. A cone has r = 3 and h = 4, so l = 5. Then V = ⅓π·9·4 = 12π and the lateral surface is πrl = 15π; total surface is 15π + 9π = 24π.