Cube, rectangular block and cylinder

The cube

A cube has edges of equal length c. Its volume is:

V = c × c × c = c³

Example: a cube with an edge length of 4 cm has a volume V = 4³ = 64 cm³.

The rectangular prism

A rectangular prism has a length L, a width l and a height h. Its volume is:

V = L × l × h

Example: a cardboard box 5 cm long, 3 cm wide and 2 cm high has a volume V = 5 × 3 × 2 = 30 cm³.

The cylinder

A cylinder of revolution has a base radius r and a height h. Its volume is:

V = π × r² × h

(the area of the base disc, π × r², multiplied by the height)

Example: a cylinder with radius r = 3 cm and height h = 10 cm has a volume of: V = π × 3² × 10 = π × 9 × 10 = 90 × π ≈ 282.7 cm³

General method

For a ‘straight’ solid (cube, rectangular prism, cylinder, prism), the volume is often calculated as follows:

V = Area of the base × height

Common pitfall to avoid

Do not confuse the radius and the diameter in the formula for a cylinder! If the question gives the diameter d, you must first calculate r = d/2 before using V = π × r² × h.