**Quantitative Ability – Cube (Detailed Concept)**

**Definition –**

A solid with six congruent square faces. A regular hexahedron.

A cube is a region of space formed by six identical square faces joined along their edges. Three edges join at each corner to form a vertex. The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids.

**Parts of a cube –**

**Face:**

Also called facets or sides. A cube has six faces which are all squares, so each face has four equal sides and all four interior angles are right angles.

**Edge:**

A line segment formed where two edges meet. A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length.

**Vertex:**

A point formed where three edges meet. A cube has 8 vertices.

**Face Diagonals:**

Face diagonals are line segments linking the opposite corners of a face. Each face has two, for a total of 12 in the cube.

**Space Diagonals:**

Space diagonals are line segments linking the opposite corners of a cube, cutting through its interior. A cube has 4 space diagonals.

**Volume enclosed by a cube:**

**Definition –**

The number of cubic units that will exactly fill a cube

**How to find the volume of a cube?**

Recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. So if the length of an edge is 4, the volume is 4 x 4 x 4 = 64

Or as a formula; Volume = s3 where: S is the length of any edge of the cube.

**Surface area of a cube:**

**Definition –**

The number of square units that will exactly cover the surface of a cube

**How to find the surface area of a cube**

Recall that a cube has all edges the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face.

Or as a formula; Surface area = 6s2 where:S is the length of an edge of the cube.

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