3D shapes and volume

• Name cube, cuboid, prism, pyramid, cylinder, sphere and cone; count faces, edges and vertices.
• Surface area = total area of all faces; draw the net if it helps.
• Cylinder: curved surface area 2πrh (given); total = 2πrh + 2πr².
• Volume of a prism = area of cross-section × length (given); cylinder πr²h (given).
• 1 cm³ = 1000 mm³; 1 m³ = 1 000 000 cm³; 1 litre = 1000 cm³.
• Higher: sphere and cone volume and surface area (given on the Higher formulae sheet).

Know your solids

A face is a flat (or curved) surface, an edge is where two faces meet, a vertex is a corner.

Add up every face

List each face and its area. A cuboid has three pairs of identical rectangles. A prism has two identical end faces plus rectangles, one for each side of the cross-section.

Curved surface plus two circles

Unrolled, the curved surface is a rectangle: one side is the circumference 2πr, the other the height h.

Cross-section × length

Both formulae below are given on the Foundation and Higher formulae sheets. A cuboid is a prism with a rectangular cross-section, so V = lwh.

Cube the conversion factor

A cube of side 1 m is 100 cm × 100 cm × 100 cm.

Given on the Higher formulae sheet

^{2 2}