Study Guides/Maths/How Many Cubes of Edge 4 cm Can Be Cut from a Larger Cube?
Study Guide · Maths

How Many Cubes of Edge 4 cm — Volume Division Problems

The volume of a cube with edge 4 cm is 4³ = 64 cm³. To find how many such cubes fit inside a larger solid, divide the volume of the larger solid by 64. For a cube of edge 12 cm: number of 4 cm cubes = 12³ ÷ 4³ = 1728 ÷ 64 = 27.

Question (Click to Flip)

How many cubes of edge 4 cm can be cut from a cube of edge 12 cm?

Answer

Volume of large cube = 12³ = 1728 cm³. Volume of small cube = 4³ = 64 cm³. Number = 1728/64 = 27. Or: (12/4)³ = 3³ = 27 cubes.

Card 1 of 3 free previews

Key Facts

Volume of cube with edge 4 cm = 4³ = 64 cm³.

Number of 4 cm cubes from a cube of edge 12 cm = (12/4)³ = 3³ = 27.

General formula: Number = (L/4) × (B/4) × (H/4) for a cuboid.

This works only when all dimensions are exactly divisible by 4.

Edge 8 cm cube → 8 small cubes; edge 16 cm → 64; edge 20 cm → 125.

Volume of a 4 cm Cube

Volume of cube = edge³ Volume of 4 cm cube = 4³ = 4 × 4 × 4 = 64 cm³

To find how many 4 cm cubes fit in a larger cube of edge a cm: Number = a³ ÷ 4³ = (a/4)³

Examples:

  1. Larger cube has edge 12 cm: Number = (12/4)³ = 3³ = 27 cubes

  2. Larger cube has edge 8 cm: Number = (8/4)³ = 2³ = 8 cubes

  3. Larger cube has edge 16 cm: Number = (16/4)³ = 4³ = 64 cubes

  4. Larger cube has edge 20 cm: Number = (20/4)³ = 5³ = 125 cubes

Cuboid Problems — 4 cm Cubes

For a cuboid (rectangular box) of dimensions l × b × h: Number of 4 cm cubes = (l/4) × (b/4) × (h/4)

Example 1: Cuboid 20 cm × 16 cm × 8 cm: Number = (20/4) × (16/4) × (8/4) = 5 × 4 × 2 = 40 cubes

Example 2: Cuboid 12 cm × 8 cm × 4 cm: Number = 3 × 2 × 1 = 6 cubes

Example 3: Cuboid 24 cm × 12 cm × 8 cm: Number = 6 × 3 × 2 = 36 cubes

Note: This method works only when each dimension is exactly divisible by 4. If not, the leftover pieces cannot form a complete 4 cm cube.

Key Formulas for Cube Problems

Cube formulas (edge = a): • Volume = a³ • Surface area = 6a² • Diagonal = a√3

For a cube of edge 4 cm: • Volume = 64 cm³ • Surface area = 6 × 16 = 96 cm² • Diagonal = 4√3 ≈ 6.93 cm

Ratio of volumes: If a large cube of edge na is cut into cubes of edge a: Number of small cubes = n³

Examples: • Large cube edge = 3a → 3³ = 27 small cubes • Large cube edge = 4a → 4³ = 64 small cubes • Large cube edge = 5a → 5³ = 125 small cubes

Questions and Answers

How many cubes of edge 4 cm can be cut from a cube of edge 12 cm?+

Volume of large cube = 12³ = 1728 cm³. Volume of small cube = 4³ = 64 cm³. Number = 1728/64 = 27. Or: (12/4)³ = 3³ = 27 cubes.

What is the volume of a cube with edge 4 cm?+

Volume = 4³ = 64 cm³.

How many 4 cm cubes fit in a cuboid of 20 × 16 × 8 cm?+

(20/4) × (16/4) × (8/4) = 5 × 4 × 2 = 40 cubes.

How do you find the number of small cubes cut from a large cube?+

Divide the volume of the large cube by the volume of the small cube. Or, for cubes: if large edge = na and small edge = a, number = n³.

More in Maths

Study Smarter with Shinyu.ai

Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.