What does it mean?
Volume counts how many equal-sized cubes fill a solid without gaps or overlaps. A cuboid’s first layer contains length × width cubes when lengths are counted in unit edges. Repeating that layer through the height gives length × width × height cubic units.
Volume measures the space inside a solid in cubic units. A cuboid with length 5 cm and width 3 cm has 15 unit cubes in one layer. With four layers, volume is 15 × 4 = 60 cm³. Thus volume = length × width × height.
Learning goal: Volume of cuboids. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Area and perimeter: the difference, examples and practice if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Convert all dimensions to the same length unit. Find the base area, then multiply by the perpendicular height. For a composite solid made of non-overlapping cuboids, calculate each volume and add. Alternatively, find a larger complete cuboid and subtract a cut-out. Write cm³ or m³ rather than a square unit.
Notation: V = length × width × height
Key rule and when to use it
Cuboid volume = length × width × perpendicular height. For non-overlapping parts, add their volumes; subtract a missing block if that is simpler.
Worked examples, step by step
Example 1: Find the volume of a 5 cm by 3 cm by 4 cm cuboid.
- Multiply 5 × 3 to find one layer.
- Multiply by 4 layers.
Answer: 60 cm³
Example 2: A box is 6 cm by 2 cm by 3 cm. Find its volume.
- One layer has 6 × 2 cubic centimetres.
- Multiply by the height 3.
Answer: 36 cm³
Example 3: A solid combines cuboids with volumes 24 cm³ and 12 cm³. Find the total volume.
- Check that the parts do not overlap.
- Add 24 and 12.
Answer: 36 cm³
Example 4: A step-shaped solid splits into 3 × 2 × 2 and 2 × 2 × 1 cuboids. Find its volume.
- Find 3 × 2 × 2 = 12.
- Find 2 × 2 × 1 = 4.
- Add the two volumes.
Answer: 16 cubic units
Example 5: Two cuboids of 4 × 3 × 2 cm and 2 × 3 × 2 cm are joined without overlap. Find their total volume.
- First volume: 4 × 3 × 2 = 24 cm³.
- Second volume: 2 × 3 × 2 = 12 cm³.
- Total = 24 + 12 = 36 cm³. Here the join also forms a 6 × 3 × 2 cuboid, which checks the result.
Common mistakes and important boundaries
Do not count only cubes or faces visible in a drawing: hidden cubes fill the interior too. Surface area is a different measurement. If one dimension is in millimetres and the others in centimetres, convert before multiplying; mixing the raw numbers creates an incorrect unit and result.
A point to explain
Volume uses three dimensions because cubes fill rows, layers and height.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Volume of Cuboids: Unit Cubes and Composite Solids — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
4 × 4 × 4 = ?
Answer and a way to check
64
Multiply the three dimensions and use cubic units.
10 × 2 × 5 = ?
Answer and a way to check
100
Multiply the three dimensions and use cubic units.
3 × 3 × 5 = ?
Answer and a way to check
45
Multiply the three dimensions and use cubic units.
2 × 7 × 4 = ?
Answer and a way to check
56
Multiply the three dimensions and use cubic units.
A small gift box is 8 cm by 5 cm by 2 cm. How much space is inside, in cm³?
Answer and a way to check
80
Multiply the three dimensions and use cubic units.
A cuboid is 8 cm by 3 cm by 2 cm. Find its volume.
Answer and a way to check
48 cm³
One layer has 8 × 3 = 24 cubes of 1 cm³. Two layers contain 48.
A cuboid has volume 72 cm³ and base area 18 cm². Find its height.
Answer and a way to check
4 cm
Height = volume ÷ base area = 72 ÷ 18 = 4.
A box is 20 mm by 3 cm by 4 cm. Find its volume in cm³.
Answer and a way to check
24 cm³
First convert 20 mm to 2 cm. Then 2 × 3 × 4 = 24 cm³.
5×2×2 + 3×2×2 = ?
Answer and a way to check
32
Split the solid into non-overlapping cuboids.
3×3×2 + 3×1×2 = ?
Answer and a way to check
24
Split the solid into non-overlapping cuboids.
6×2×1 + 2×2×1 = ?
Answer and a way to check
16
Split the solid into non-overlapping cuboids.
3×2×3 + 1×2×3 = ?
Answer and a way to check
24
Split the solid into non-overlapping cuboids.
Volume of Cuboids: Unit Cubes and Composite Solids — answer key
64 Multiply the three dimensions and use cubic units.
100 Multiply the three dimensions and use cubic units.
45 Multiply the three dimensions and use cubic units.
56 Multiply the three dimensions and use cubic units.
80 Multiply the three dimensions and use cubic units.
48 cm³ One layer has 8 × 3 = 24 cubes of 1 cm³. Two layers contain 48.
4 cm Height = volume ÷ base area = 72 ÷ 18 = 4.
24 cm³ First convert 20 mm to 2 cm. Then 2 × 3 × 4 = 24 cm³.
32 Split the solid into non-overlapping cuboids.
24 Split the solid into non-overlapping cuboids.
16 Split the solid into non-overlapping cuboids.
24 Split the solid into non-overlapping cuboids.
Questions students and parents ask
Does surface area tell me how much fits inside?
No. Surface area measures the outside in square units. Volume measures space in cubic units. A capacity question may use litres: 1,000 cm³ = 1 L.
If I double every dimension, does volume double?
No. Each of three factors doubles, so the volume becomes 2 × 2 × 2 = 8 times as large. Doubling only one dimension doubles volume.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Area and perimeter: the difference, examples and practice. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Build two layers of cubes and count one complete layer first. Ask how the multiplication records the rows, columns and layers.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
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About this guide
Based on BananaLearn’s Grade 5 course lesson “Volume of cuboids” and its related lesson “Composite volume”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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