Volume of Cube
A cube is a special three-dimensional shape where all six faces are identical squares. Dice, ice cubes, Rubik's cubes, and sugar cubes are common examples of cubes.
The volume of a cube measures how much space is inside the cube. Since all edges of a cube are equal, you only need one measurement — the side length — to calculate the volume.
In Class 5, learning the volume of a cube builds a strong foundation for understanding 3D shapes and their properties.
What is Volume of Cube - Class 5 Maths (Measurement)?
The volume of a cube is the total space enclosed within its six square faces. Since every edge of a cube has the same length, the volume is found by multiplying the side length by itself three times.
Properties of a cube:
- All 6 faces are equal squares.
- All 12 edges are of equal length.
- It has 8 vertices (corners).
- Each angle is a right angle (90°).
Volume of Cube Formula
Volume of Cube = Side × Side × Side = Side³
V = s³
Here, s represents the length of one edge of the cube.
| Side Length | Volume (s³) |
|---|---|
| 1 cm | 1 cm³ |
| 2 cm | 8 cm³ |
| 3 cm | 27 cm³ |
| 4 cm | 64 cm³ |
| 5 cm | 125 cm³ |
| 10 cm | 1,000 cm³ |
Finding the side from volume: If volume is known, the side length is the cube root of the volume.
Solved Examples
Example 1: Example 1: Basic Cube Volume
Problem: Find the volume of a cube with side 6 cm.
Solution:
Step 1: V = s × s × s
Step 2: V = 6 × 6 × 6
Step 3: V = 216
Answer: Volume = 216 cm³
Example 2: Example 2: Ice Cube Problem
Problem: An ice cube has each edge measuring 3 cm. What is its volume?
Solution:
Step 1: V = s³ = 3 × 3 × 3
Step 2: V = 27
Answer: Volume of the ice cube = 27 cm³
Example 3: Example 3: Dice Problem
Problem: Aman has a dice with side 2 cm. Find the volume of the dice.
Solution:
Step 1: V = 2 × 2 × 2
Step 2: V = 8
Answer: Volume of the dice = 8 cm³
Example 4: Example 4: Volume in Metres
Problem: A cubic water tank has each side measuring 2 m. Calculate its volume and the litres of water it can hold. (1 m³ = 1,000 litres)
Solution:
Step 1: V = 2 × 2 × 2 = 8 m³
Step 2: Convert to litres: 8 × 1,000 = 8,000 litres
Answer: Volume = 8 m³ = 8,000 litres
Example 5: Example 5: Comparing Two Cubes
Problem: Cube A has side 4 cm. Cube B has side 5 cm. How much more space does Cube B have?
Solution:
Step 1: Volume of Cube A = 4³ = 64 cm³
Step 2: Volume of Cube B = 5³ = 125 cm³
Step 3: Difference = 125 − 64 = 61 cm³
Answer: Cube B has 61 cm³ more space than Cube A.
Example 6: Example 6: Multiple Cubes
Problem: Priya has 5 sugar cubes. Each sugar cube has a side of 1 cm. What is the total volume of all the sugar cubes?
Solution:
Step 1: Volume of one sugar cube = 1 × 1 × 1 = 1 cm³
Step 2: Total volume = 5 × 1 = 5 cm³
Answer: Total volume = 5 cm³
Example 7: Example 7: Side from Volume
Problem: A cube has a volume of 125 cm³. Find the side length.
Solution:
Step 1: V = s³, so we need s × s × s = 125
Step 2: Think: 5 × 5 × 5 = 125
Answer: Side = 5 cm
Example 8: Example 8: Gift Box Problem
Problem: Meera wraps a cubic gift box with side 12 cm. What is the volume of the gift box?
Solution:
Step 1: V = 12 × 12 × 12
Step 2: 12 × 12 = 144, then 144 × 12 = 1,728
Answer: Volume = 1,728 cm³
Example 9: Example 9: Cube vs Cuboid
Problem: A cube has side 7 cm. A cuboid has length 10 cm, breadth 7 cm, and height 5 cm. Which has the greater volume?
Solution:
Step 1: Volume of cube = 7³ = 343 cm³
Step 2: Volume of cuboid = 10 × 7 × 5 = 350 cm³
Step 3: Compare: 350 > 343
Answer: The cuboid has the greater volume by 7 cm³.
Example 10: Example 10: Volume in Millimetres
Problem: A tiny cube has side 15 mm. Find its volume.
Solution:
Step 1: V = 15 × 15 × 15
Step 2: 15 × 15 = 225, then 225 × 15 = 3,375
Answer: Volume = 3,375 mm³
Real-World Applications
Real-Life Uses of Volume of a Cube
- Storage: Calculating how much a cubic container or box can hold.
- Cooking: Measuring the volume of cube-shaped moulds for sweets or ice.
- Construction: Estimating the volume of cube-shaped blocks or pillars.
- Games: Understanding the size of dice and puzzle cubes.
Key Points to Remember
- A cube has 6 equal square faces, 12 equal edges, and 8 vertices.
- Volume of cube = s × s × s = s³, where s is the side length.
- Volume is always in cubic units (cm³, m³, mm³).
- If the side doubles, the volume becomes 8 times larger (2³ = 8).
- To find the side from the volume, take the cube root of the volume.
- A cube is a special type of cuboid where all three dimensions are equal.
- 1 cm³ = 1 millilitre (mL) and 1 m³ = 1,000 litres.
Practice Problems
- Find the volume of a cube with side 9 cm.
- A Rubik's cube has an edge of 6 cm. Calculate its volume.
- Rahul has a cube-shaped aquarium with side 30 cm. How many cm³ of water can it hold?
- A cube has a volume of 64 cm³. What is the length of each side?
- How many small cubes of side 1 cm can fit inside a larger cube of side 4 cm?
- A cube of side 10 cm is cut into smaller cubes of side 2 cm. How many smaller cubes are formed?
- Neha has a cubic container of side 0.5 m. How many litres of milk can it hold?
- A cube has a volume of 1,000 cm³. Find its side length.
Frequently Asked Questions
Q1. What is the formula for the volume of a cube?
Volume of a cube = side × side × side = s³. You only need one measurement since all edges of a cube are equal.
Q2. What is the difference between a cube and a cuboid?
A cube has all 6 faces as equal squares and all 12 edges equal. A cuboid has 6 rectangular faces and can have three different edge lengths. Every cube is a cuboid, but not every cuboid is a cube.
Q3. If the side of a cube is doubled, what happens to the volume?
The volume becomes 8 times the original. For example, if the side changes from 3 cm to 6 cm, volume changes from 27 cm³ to 216 cm³ (which is 8 × 27).
Q4. How do you find the side of a cube when the volume is given?
Find which number multiplied by itself three times gives the volume. For example, if V = 343 cm³, then s = 7 because 7 × 7 × 7 = 343.
Q5. What is 1 cubic centimetre equal to in millilitres?
1 cm³ = 1 mL (millilitre). So a cube of side 10 cm has volume 1,000 cm³ = 1,000 mL = 1 litre.
Q6. How many unit cubes fit inside a cube of side n?
n³ unit cubes fit inside. For a cube of side 5 cm, you can fit 5 × 5 × 5 = 125 cubes of side 1 cm.
Q7. Can a cube have a fractional side length?
Yes. For example, a cube with side 2.5 cm has volume 2.5 × 2.5 × 2.5 = 15.625 cm³. The formula works for any positive number.
Q8. What are some examples of cubes in daily life?
Dice, sugar cubes, ice cubes, Rubik's cubes, and some gift boxes are common cube shapes found in everyday life.
