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Volume of a Cube

一句话总结： The volume of a cube (the amount of space inside it) is found by multiplying the side length by itself three times: side × side × side.

为什么成立

Volume tells us how much space something takes up or how much it can hold, like how much sand fills a box or how much water fits in a tank. A cube is a 3D shape with six identical square faces, so all its edges are the same length, which makes it the perfect shape for learning volume. Once you understand cubes, finding the volume of boxes, rooms and other shapes becomes much easier.

可以这样理解： Imagine building a cube out of small 1 cm sugar cubes. If each edge of your big cube is 3 sugar cubes long, the bottom layer is 3 rows of 3, which is 9 sugar cubes. You need 3 of these layers to reach the top, so 9 × 3 = 27 sugar cubes. Counting the sugar cubes is the same as working out side × side × side. (不适用的情况：The sugar-cube picture only works neatly when the side length is a whole number. A cube with sides of 2.5 cm cannot be built from whole 1 cm blocks, but the rule side × side × side still works perfectly: 2.5 × 2.5 × 2.5 = 15.625 cm³.)

例题详解

A wooden block is a cube with sides 4 cm long. What is its volume?

  1. Write the rule: volume = side × side × side.
  2. Put in the side length: volume = 4 × 4 × 4.
  3. Multiply the first two: 4 × 4 = 16. This is the area of one face, or one layer of 1 cm blocks.
  4. Multiply by the height: 16 × 4 = 64.
  5. Add cubic units, because volume measures 3D space: 64 cm³ (said 'cubic centimetres').

答案： The volume of the cube is 64 cm³.

常见错误

  • Multiplying the side by 3 (4 × 3 = 12) instead of multiplying the side by itself three times (4 × 4 × 4 = 64).
  • Stopping after side × side, which only gives the area of one face, so remember to multiply by the side one more time.
  • Writing square units like cm² instead of cubic units like cm³, so always use the small 3 for volume.
  • Mixing up volume and surface area (the total area of all six faces), so check whether the question asks for space inside or the outside covering.

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A cube has sides 3 cm long. What is its volume?

家长常见问题

What year do kids learn the volume of a cube?

Children usually start by counting cubes to measure volume, then learn the formula around Year 5–6 in the UK, Years 6–7 in Australia and Grade 5 in the US. Cubed numbers and working backwards from a volume often come in Years 6–7 (UK and Australia) or Grades 5–6 (US).

How can I help my child with volume of a cube at home?

Use dice, sugar cubes or building blocks to build small cubes and count how many blocks are inside. Then ask your child to check the count by multiplying side × side × side so they see why the rule works.

What is the difference between area and volume?

Area measures flat space, like the surface of a page, and uses square units such as cm². Volume measures 3D space, like the inside of a box, and uses cubic units such as cm³.

Why is it called 'cubed' when you multiply a number by itself three times?

Because a number multiplied by itself three times gives exactly the volume of a cube with that side length. For example, 4 cubed (written 4³) is 4 × 4 × 4 = 64, the volume of a cube with 4 cm sides.