3D Solids

V = a³ — A cube has six identical square faces, twelve equal edges and eight vertices.

V = l × w × h — A cuboid is a box with three pairs of rectangular faces. Its volume is length × width × height.

V = (4⁄3) πr³ — A sphere is the set of all points in space at distance r from the centre — a perfectly round ball.

V = (2⁄3) πr³ — A hemisphere is half a sphere. Its total surface area includes the curved dome plus the flat circular base.

V = πr²h — A cylinder has two parallel circular bases joined by a curved surface. Unrolled, the curved surface is a rectangle 2πr wide.

V = (1⁄3) πr²h — A right circular cone tapers from a circular base to an apex. Its slant height l comes from the Pythagorean theorem.

V = (1⁄3) a²h — A square pyramid has a square base and four triangular faces meeting at the apex. Its volume is one third of the matching prism.