Volume of Cube Explained with Side Length Examples

Volume of Cube is the space occupied by a cube. It is calculated by multiplying its length, breadth and height, which are all equal. Therefore, the volume is the cube of its side. This page covers the formula, unit conversion, reverse calculations, scaling rules and solved volume of cube problems.

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What Is the Volume of a Cube?

The volume of a cube is the space enclosed by it and is given by V = a^3, where a is the length of one edge.

A cube has six equal square faces and all its edges have the same length. Since volume = length × breadth × height, V = a × a × a = a^3. If the side is measured in centimetres, the volume is in cubic centimetres (cm^3); if it is measured in metres, the volume is in cubic metres (m^3).

Volume of Cube Video Lessons

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Cube Volume, Surface Area and Diagonal

Learn how to calculate a cube’s volume, surface area, and diagonal using the relevant formulas and understand the relationship between its dimensions and measurements.

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Volume of Cube Formula & Tricks

Important Formulas

Volume of a cube
V = a^3

Here, V is the volume and a is the length of each equal edge.

Volume using three dimensions
V = l × b × h; for a cube, l = b = h = a

Substituting equal dimensions gives V = a × a × a = a^3.

Side from volume
a = ∛V

The side of a cube is the cube root of its volume.

Change in volume
If the side becomes ka, the new volume is k^3V

Volume changes as the cube of the side-length scale factor.

Quick Tricks

Keep all dimensions in one unit

Convert the side to the required unit before cubing it. Cubing a conversion factor is necessary because volume is three-dimensional.

Example: A side of 2 m is 200 cm. Its volume is 2^3 = 8 m^3, or 200^3 = 8,000,000 cm^3.
Use cube numbers for reverse questions

When the volume is given, identify its cube root directly instead of testing several possible side lengths.

Example: If V = 15,625 cm^3, then a = ∛15,625 = 25 cm.
Apply the scale factor to volume

If every edge is multiplied by k, multiply the original volume by k^3, not by k.

Example: If the side doubles, the volume becomes 2^3 = 8 times the original volume.

Volume of Cube Concepts

Calculating Volume from the Side

To find the volume of a cube, cube the length of its edge: V = a^3.

Multiply the side by itself three times. For a side of 7 cm, V = 7 × 7 × 7 = 343 cm^3. The unit is also raised to the third power.

Example: For a cube with side 12 m, volume = 12^3 = 1,728 m^3.

Finding the Side from the Volume

When the volume is known, find the side by taking its cube root: a = ∛V.

The volume must be expressed in cubic units before taking the cube root. For example, ∛1,000 cm^3 = 10 cm because 10^3 = 1,000.

Example: A cube has volume 4,096 cm^3. Its side is ∛4,096 = 16 cm.

Unit Conversion in Cube Volume

For cubic units, the length conversion factor must be cubed.

Since 1 m = 100 cm, 1 m^3 = 100^3 cm^3 = 1,000,000 cm^3. Similarly, 1 cm^3 = 1,000 mm^3 because 1 cm = 10 mm.

Example: A cube with side 50 cm has volume 125,000 cm^3, which is 0.125 m^3.

Effect of Changing the Edge

If the edge changes from a to ka, the volume changes from a^3 to k^3a^3.

A 10% increase in the side makes the new side 1.1a, so the new volume is 1.1^3V = 1.331V. Thus, the volume increases by 33.1%.

Example: If the side changes from 4 cm to 8 cm, the volume changes from 64 cm^3 to 512 cm^3, which is 8 times.

Cube Made from Smaller Cubes

If a cube of side A is divided into smaller cubes of side a, the number of smaller cubes is (A/a)^3.

The ratio A/a gives the number of small cubes along each edge. Cubing this ratio gives the total number of small cubes, provided A and a use the same unit.

Example: A cube of side 12 cm is divided into cubes of side 3 cm. Number of small cubes = (12/3)^3 = 4^3 = 64.

Volume of Cube Visual Guide & Data

Use the table and chart below to understand the data better.

Common Cube Sides and Volumes

The table shows volumes obtained by cubing the side length.

Side Volume
2 cm 8 cm^3
3 cm 27 cm^3
4 cm 64 cm^3
5 cm 125 cm^3
10 cm 1,000 cm^3

Note: The volume unit is the cube of the side unit.

Cube with Equal Edge Lengths

Visual guide: Cube with Equal Edge Lengths
Length: a Breadth: a Height: a
All three dimensions of a cube are equal, so its volume is a × a × a = a^3.

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Practice Volume of Cube Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Volume of Cube Revision Points

Use these formulas and rules for quick revision.

  • Volume of a cube = side^3 = a^3.
  • Side of a cube = cube root of volume = ∛V.
  • The volume is measured in cubic units such as cm^3, m^3 or mm^3.
  • If 1 m = 100 cm, then 1 m^3 = 1,000,000 cm^3.
  • If the side is multiplied by k, the volume is multiplied by k^3.
  • Number of smaller cubes = (side of large cube ÷ side of small cube)^3.

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Volume of Cube FAQs

What is the volume of a cube with side 6 cm?

V = 6^3 = 6 × 6 × 6 = 216 cm^3.

What is the volume of a cube with side 1.5 m?

V = 1.5^3 = 3.375 m^3.

How do you find the side of a cube whose volume is 729 cm^3?

Take the cube root: a = ∛729 = 9 cm.

How many cubic centimetres are in 2 m^3?

Since 1 m^3 = 1,000,000 cm^3, 2 m^3 = 2,000,000 cm^3.

If the side of a cube increases by 20%, what happens to its volume?

The new volume is (1.2)^3 = 1.728 times the original volume. Therefore, the volume increases by 72.8%.

A cube has volume 8,000 cm^3. What is its edge length?

The edge length is ∛8,000 = 20 cm.

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