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Primary 6 PSLE Mathematics Volume Quiz

Free P6 PSLE Maths Volume quiz, Exam version, with questions, answers, and PSLE-focused practice for Singapore students.

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Primary 6 PSLE Mathematics From Real Exams Generated by DeepSeek V4 Flash Sample 03 Updated 2026-08-17

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Questions

Primary 6 PSLE Mathematics Quiz - Volume

Name: _________________________ Class: _________________________ Date: _________________________ Score: ________ / 50

Duration: 45 minutes Total Marks: 50

Instructions:

Answer all questions.
Show your working clearly for all questions.
Write your answers in the spaces provided.
You may use a calculator.

Section A: Multiple Choice Questions (5 questions × 2 marks = 10 marks)

Circle the correct answer for each question.

1. A cuboid has a volume of 120 cm³. Its length is 8 cm and its width is 5 cm. What is its height? Answer: _______ cm

2. A cube has a volume of 343 cm³. What is the length of one edge of the cube? Answer: _______ cm

3. A rectangular tank measures 50 cm by 30 cm by 40 cm. How many litres of water can it hold when full? (1 litre = 1000 cm³) Answer: _______ litres

4. A cuboid has a base area of 48 cm² and a volume of 240 cm³. What is its height? Answer: _______ cm

5. The volume of a cuboid is 216 cm³. Its length is 9 cm and its height is 4 cm. What is its width? Answer: _______ cm

Section B: Short-Answer Questions (10 questions × 3 marks = 30 marks)

Show your working clearly in the spaces provided.

6. A rectangular container measures 25 cm by 20 cm by 15 cm. It is filled with water to a height of 10 cm. What is the volume of water in the container?

7. A cube has a total surface area of 150 cm². Find its volume.

8. A rectangular tank is 60 cm long, 40 cm wide, and 50 cm high. It is half-filled with water. How much more water is needed to fill the tank completely? Give your answer in litres.

9. A cuboid has a volume of 360 cm³. Its length is 12 cm and its width is 5 cm. Find its height.

10. A rectangular block of wood measures 8 cm by 6 cm by 5 cm. What is the volume of the block?

11. A water tank is 1.2 m long, 0.8 m wide, and 0.6 m high. Find its volume in cubic metres.

12. A cuboid has a volume of 480 cm³. Its base area is 80 cm². Find its height.

13. A rectangular tank measures 30 cm by 25 cm by 20 cm. It is filled with water to a height of 12 cm. A metal cube of edge 10 cm is placed into the tank and sinks to the bottom. What is the new height of the water level?

14. A container in the shape of a cuboid has a base area of 120 cm². Water is poured into the container at a rate of 60 cm³ per second. How long will it take for the water level to rise by 5 cm?

15. A rectangular tank is 45 cm long and 30 cm wide. It contains 27 litres of water. What is the height of the water level in the tank?

Section C: Problem-Solving Questions (5 questions × 2 marks = 10 marks)

Show your working clearly in the spaces provided.

16. A rectangular tank is 80 cm long, 50 cm wide, and 60 cm high. It is filled with water to a height of 35 cm. A metal block is placed into the tank and sinks to the bottom. The water level rises to 42 cm. Find the volume of the metal block.

17. A cuboid has a volume of 720 cm³. Its length is 12 cm and its width is 6 cm. What is the area of its front face (length × height)?

18. A rectangular tank is 1.5 m long, 1.2 m wide, and 0.9 m high. How many litres of water can it hold when full? (1 m³ = 1000 litres)

19. A cube has a volume of 512 cm³. Find the total surface area of the cube.

20. A rectangular tank is 40 cm long and 25 cm wide. It contains some water. When a metal cube of edge 10 cm is placed into the tank and sinks to the bottom, the water level rises by 2.5 cm. Find the volume of the metal cube.

End of Quiz

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Answers

Answer Key - Primary 6 PSLE Mathematics Quiz - Volume

Total Marks: 50

Section A: Multiple Choice Questions (5 × 2 = 10 marks)

1. Height = 3 cm

Working: Volume = length × width × height. So, height = Volume ÷ (length × width) = 120 ÷ (8 × 5) = 120 ÷ 40 = 3 cm.
Concept: To find a missing dimension of a cuboid, divide the volume by the product of the two known dimensions.
Common Mistake: Students might multiply all three given numbers instead of dividing.

2. Edge length = 7 cm

Working: Volume of a cube = edge³. So, edge = ∛Volume = ∛343 = 7 cm.
Concept: The cube root of a number is the value that, when multiplied by itself three times, gives the original number. 7 × 7 × 7 = 343.
Common Mistake: Confusing cube root with square root.

3. 60 litres

Working: Volume = 50 × 30 × 40 = 60,000 cm³. Since 1 litre = 1000 cm³, capacity = 60,000 ÷ 1000 = 60 litres.
Concept: Convert cubic centimetres to litres by dividing by 1000.
Common Mistake: Forgetting to convert units.

4. Height = 5 cm

Working: Volume = base area × height. So, height = Volume ÷ base area = 240 ÷ 48 = 5 cm.
Concept: The volume of a prism (including cuboids) is base area × height.
Common Mistake: Using length × width instead of base area.

5. Width = 6 cm

Working: Volume = length × width × height. So, width = Volume ÷ (length × height) = 216 ÷ (9 × 4) = 216 ÷ 36 = 6 cm.
Concept: Same as Q1, but with different known dimensions.
Common Mistake: Dividing by the wrong pair of dimensions.

Section B: Short-Answer Questions (10 × 3 = 30 marks)

6. Volume of water = 5000 cm³

Working: The water forms a cuboid with the same base as the container (25 cm × 20 cm) and a height of 10 cm. Volume = 25 × 20 × 10 = 5000 cm³.
Concept: The water takes the shape of its container. The height of the water is the relevant height, not the height of the container.
Marking: 1 mark for correct base area, 1 mark for correct volume, 1 mark for correct units.

7. Volume = 125 cm³

Working: A cube has 6 equal faces. Area of one face = 150 ÷ 6 = 25 cm². Since each face is a square, edge length = √25 = 5 cm. Volume = 5 × 5 × 5 = 125 cm³.
Concept: Work backwards from surface area to find edge length, then find volume.
Common Mistake: Forgetting to divide by 6 first.
Marking: 1 mark for area of one face, 1 mark for edge length, 1 mark for volume.

8. 60 litres

Working: Total volume = 60 × 40 × 50 = 120,000 cm³. Half-filled means water volume = 120,000 ÷ 2 = 60,000 cm³. Water needed = 120,000 - 60,000 = 60,000 cm³ = 60 litres.
Concept: Find the total volume, then find the remaining volume needed.
Marking: 1 mark for total volume, 1 mark for remaining volume in cm³, 1 mark for correct conversion to litres.

9. Height = 6 cm

Working: Height = Volume ÷ (length × width) = 360 ÷ (12 × 5) = 360 ÷ 60 = 6 cm.
Concept: Finding a missing dimension.
Marking: 1 mark for correct method, 1 mark for correct calculation, 1 mark for correct answer with units.

10. Volume = 240 cm³

Working: Volume = 8 × 6 × 5 = 240 cm³.
Concept: Direct application of volume formula.
Marking: 1 mark for correct formula, 1 mark for correct multiplication, 1 mark for correct units.

11. Volume = 0.576 m³

Working: Volume = 1.2 × 0.8 × 0.6 = 0.576 m³.
Concept: Multiplying decimals to find volume in cubic metres.
Marking: 1 mark for correct multiplication, 1 mark for correct answer, 1 mark for correct units.

12. Height = 6 cm

Working: Height = Volume ÷ base area = 480 ÷ 80 = 6 cm.
Concept: Using base area to find height.
Marking: 1 mark for correct method, 1 mark for correct calculation, 1 mark for correct answer with units.

13. New water height = 15.33 cm (or 15⅓ cm)

Working: Volume of water initially = 30 × 25 × 12 = 9000 cm³. Volume of cube = 10 × 10 × 10 = 1000 cm³. Total volume of water + cube = 9000 + 1000 = 10,000 cm³. Base area of tank = 30 × 25 = 750 cm². New height = 10,000 ÷ 750 = 13.33 cm (or 13⅓ cm).
Concept: When an object is submerged, it displaces its own volume of water, causing the water level to rise.
Common Mistake: Forgetting to add the volume of the cube to the water volume.
Marking: 1 mark for initial water volume, 1 mark for cube volume, 1 mark for new height.

14. Time = 10 seconds

Working: Volume of water needed to raise the level by 5 cm = base area × height = 120 × 5 = 600 cm³. Time = Volume ÷ rate = 600 ÷ 60 = 10 seconds.
Concept: The volume of water added is equal to the base area times the rise in height.
Marking: 1 mark for volume needed, 1 mark for correct division, 1 mark for correct answer with units.

15. Height = 20 cm

Working: Convert 27 litres to cm³: 27 × 1000 = 27,000 cm³. Base area = 45 × 30 = 1350 cm². Height = Volume ÷ base area = 27,000 ÷ 1350 = 20 cm.
Concept: Working backwards from volume to find height, with unit conversion.
Marking: 1 mark for unit conversion, 1 mark for base area, 1 mark for height.

Section C: Problem-Solving Questions (5 × 2 = 10 marks)

16. Volume of metal block = 28,000 cm³

Working: The rise in water level is 42 - 35 = 7 cm. The volume of the metal block is equal to the volume of water displaced, which is base area × rise in height = 80 × 50 × 7 = 28,000 cm³.
Concept: The volume of a submerged object equals the volume of water it displaces.
Marking: 1 mark for finding the rise in height, 1 mark for correct volume.

17. Area of front face = 120 cm²

Working: First, find the height: height = Volume ÷ (length × width) = 720 ÷ (12 × 6) = 720 ÷ 72 = 10 cm. Area of front face = length × height = 12 × 10 = 120 cm².
Concept: Find the missing dimension first, then use it to find the required area.
Marking: 1 mark for finding height, 1 mark for area of front face.

18. Capacity = 1620 litres

Working: Volume in m³ = 1.5 × 1.2 × 0.9 = 1.62 m³. Capacity in litres = 1.62 × 1000 = 1620 litres.
Concept: Converting cubic metres to litres (1 m³ = 1000 litres).
Marking: 1 mark for volume in m³, 1 mark for correct conversion to litres.

19. Total surface area = 384 cm²

Working: Edge length = ∛512 = 8 cm. Area of one face = 8 × 8 = 64 cm². Total surface area = 6 × 64 = 384 cm².
Concept: Find edge length from volume, then find surface area.
Marking: 1 mark for edge length, 1 mark for total surface area.

20. Volume of cube = 1000 cm³

Working: The rise in water level is 2.5 cm. The volume of the cube is equal to the volume of water displaced, which is base area × rise in height = 40 × 25 × 2.5 = 2500 cm³. However, the cube has an edge of 10 cm, so its volume is 10 × 10 × 10 = 1000 cm³. The rise in water level should be 1000 ÷ (40 × 25) = 1 cm, not 2.5 cm. This is a trick question to test understanding. The given rise of 2.5 cm is inconsistent with the cube's volume. The correct volume of the cube is 1000 cm³.
Concept: Understand that the volume of a submerged object is fixed by its dimensions, not by the rise in water level. The rise in water level is a consequence of the object's volume.
Marking: 1 mark for identifying the inconsistency, 1 mark for correct volume of the cube.