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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 04 Updated 2026-08-17

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Questions

Primary 6 PSLE Mathematics Quiz - Volume

Name: _________________________ Class: _________________________ Date: _________________________ Score: ________ / 40

Duration: 45 minutes Total Marks: 40

Instructions:

This quiz consists of 20 questions on the topic of Volume of Cubes and Cuboids.
Answer all questions. Show your working clearly for all questions.
You may use a calculator.
Write your answers in the spaces provided.

Section A: Multiple-Choice Questions (Questions 1 to 5)

Choose the correct answer and write its letter (A, B, C or D) in the box. (2 marks each)

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

A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Answer: \boxed{\phantom{A}}

2. A cube has a volume of 64 cm³. What is the length of one edge of the cube?

A) 4 cm
B) 6 cm
C) 8 cm
D) 16 cm

Answer: \boxed{\phantom{A}}

3. The volume of a cuboid is 240 cm³. The area of its base is 60 cm². What is its height?

A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Answer: \boxed{\phantom{A}}

4. A rectangular tank measures 30 cm by 20 cm by 15 cm. It is completely filled with water. What is the volume of water in the tank?

A) 900 cm³
B) 6000 cm³
C) 9000 cm³
D) 12 000 cm³

Answer: \boxed{\phantom{A}}

5. A cuboid has a square base of side 6 cm. Its volume is 216 cm³. What is its height?

A) 4 cm
B) 5 cm
C) 6 cm
D) 7 cm

Answer: \boxed{\phantom{A}}

Section B: Short-Answer Questions (Questions 6 to 15)

Show your working clearly. Write your answer in the space provided. (2 marks each)

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

Answer: __________________ cm

Working:

7. A cube has a volume of 125 cm³. Find the total surface area of the cube.

Answer: __________________ cm²

Working:

8. A rectangular tank is 40 cm long and 25 cm wide. It contains water to a depth of 12 cm. What is the volume of water in the tank?

Answer: __________________ cm³

Working:

9. A cuboid has a volume of 480 cm³. Its length is 10 cm and its width is 8 cm. Find its height.

Answer: __________________ cm

Working:

10. A cube has an edge length of 9 cm. Find its volume.

Answer: __________________ cm³

Working:

11. A rectangular tank measures 50 cm by 30 cm by 20 cm. How many litres of water can it hold when full? (1 litre = 1000 cm³)

Answer: __________________ litres

Working:

12. A cuboid has a square base. The area of the base is 49 cm². The volume of the cuboid is 343 cm³. Find the height of the cuboid.

Answer: __________________ cm

Working:

13. A rectangular tank is 60 cm long and 40 cm wide. It is filled with water to a height of 25 cm. All the water is poured into another rectangular tank that is 50 cm long and 30 cm wide. What is the height of the water in the second tank?

Answer: __________________ cm

Working:

14. A solid cuboid has dimensions 15 cm by 10 cm by 8 cm. What is the volume of the cuboid?

Answer: __________________ cm³

Working:

15. A cube has a volume of 216 cm³. Find the length of one edge of the cube.

Answer: __________________ cm

Working:

Section C: Problem-Solving Questions (Questions 16 to 20)

Show your working clearly. Write your answer in the space provided. (4 marks each)

16. A rectangular tank measuring 50 cm by 40 cm by 30 cm is $\frac{3}{5}$ filled with water.

Diagram for Q16 (P6 Maths)

Generated diagram for Q16.

(a) What is the volume of water in the tank? [2 marks]

Answer (a): __________________ cm³

(b) How much more water is needed to fill the tank completely? [2 marks]

Answer (b): __________________ cm³

Working:

17. A rectangular tank is 80 cm long and 50 cm wide. It contains some water. When a metal cube is placed into the tank, the water level rises by 4 cm.

Diagram for Q17 (P6 Maths)

Generated diagram for Q17.

(a) Find the volume of the metal cube. [2 marks]

Answer (a): __________________ cm³

(b) Find the length of one edge of the cube. [2 marks]

Answer (b): __________________ cm

Working:

18. A rectangular tank measuring 60 cm by 40 cm by 35 cm is $\frac{2}{7}$ filled with water. Water is then poured into the tank at a rate of 2 litres per minute.

Diagram for Q18 (P6 Maths)

Generated diagram for Q18.

(a) What is the volume of water in the tank at first? [2 marks]

Answer (a): __________________ cm³

(b) How long will it take to fill the tank completely? Give your answer in minutes. [2 marks]

Answer (b): __________________ minutes

Working:

19. A rectangular tank is 90 cm long and 60 cm wide. It is filled with water to a height of 40 cm. Some water is then poured out until the water level drops to 25 cm.

Diagram for Q19 (P6 Maths)

Generated diagram for Q19.

(a) What is the volume of water poured out? [2 marks]

Answer (a): __________________ cm³

(b) The water poured out is then used to fill some identical cubical containers of edge 10 cm. How many such containers can be filled completely? [2 marks]

Answer (b): __________________

Working:

20. A rectangular tank, measuring 100 cm by 60 cm by 50 cm, is $\frac{3}{4}$ filled with water. A metal cuboid of dimensions 20 cm by 15 cm by 10 cm is placed into the tank and sinks to the bottom.

Diagram for Q20 (P6 Maths)

Generated diagram for Q20.

(a) What is the volume of water in the tank at first? [2 marks]

Answer (a): __________________ cm³

(b) After the metal cuboid is placed in the tank, what is the new height of the water level? [2 marks]

Answer (b): __________________ cm

Working:

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Answers

Primary 6 PSLE Mathematics Quiz - Volume: Answer Key

Total Marks: 40

Section A: Multiple-Choice Questions (Questions 1 to 5)

(2 marks each)

1. Answer: B) 3 cm

Working: Height = Volume ÷ (Length × Width) = 120 cm³ ÷ (8 cm × 5 cm) = 120 cm³ ÷ 40 cm² = 3 cm.
Concept: To find a missing dimension of a cuboid when the volume and the other two dimensions are known, divide the volume by the product of the two known dimensions.
Common Mistake: Students might multiply all three numbers instead of dividing.

2. Answer: A) 4 cm

Working: Edge length = ∛Volume = ∛64 cm³ = 4 cm.
Concept: The volume of a cube is edge × edge × edge (edge³). To find the edge length from the volume, find the cube root. 4 × 4 × 4 = 64.
Common Mistake: Students might find the square root (8) instead of the cube root.

3. Answer: C) 4 cm

Working: Height = Volume ÷ Base Area = 240 cm³ ÷ 60 cm² = 4 cm.
Concept: The volume of a cuboid is Base Area × Height. Therefore, Height = Volume ÷ Base Area.
Common Mistake: Students might try to find the length and width separately, which is unnecessary.

4. Answer: C) 9000 cm³

Working: Volume = Length × Width × Height = 30 cm × 20 cm × 15 cm = 9000 cm³.
Concept: The volume of a rectangular tank is found by multiplying its length, width, and height.
Common Mistake: Students might forget to multiply all three dimensions or make a calculation error (e.g., 30 × 20 = 600, 600 × 15 = 9000).

5. Answer: C) 6 cm

Working: Area of square base = side × side = 6 cm × 6 cm = 36 cm². Height = Volume ÷ Base Area = 216 cm³ ÷ 36 cm² = 6 cm.
Concept: First find the area of the square base, then use the formula Height = Volume ÷ Base Area.
Common Mistake: Students might assume the height is the same as the side of the square base without calculating.

Section B: Short-Answer Questions (Questions 6 to 15)

(2 marks each)

6. Answer: 6 cm

Working: Width = Volume ÷ (Length × Height) = 360 cm³ ÷ (12 cm × 5 cm) = 360 cm³ ÷ 60 cm² = 6 cm.
Concept: To find a missing dimension, divide the volume by the product of the other two dimensions.
Marking: 1 mark for correct method, 1 mark for correct answer.

7. Answer: 150 cm²

Working: Edge length = ∛125 cm³ = 5 cm. Area of one face = 5 cm × 5 cm = 25 cm². Total surface area = 6 × 25 cm² = 150 cm².
Concept: A cube has 6 identical square faces. First find the edge length using the cube root, then find the area of one face, and finally multiply by 6.
Marking: 1 mark for finding edge length, 1 mark for correct total surface area.

8. Answer: 12 000 cm³

Working: Volume of water = Length × Width × Depth of water = 40 cm × 25 cm × 12 cm = 12 000 cm³.
Concept: When finding the volume of water in a tank, use the depth of the water as the height.
Marking: 1 mark for correct method, 1 mark for correct answer.

9. Answer: 6 cm

Working: Height = Volume ÷ (Length × Width) = 480 cm³ ÷ (10 cm × 8 cm) = 480 cm³ ÷ 80 cm² = 6 cm.
Concept: To find a missing dimension, divide the volume by the product of the other two dimensions.
Marking: 1 mark for correct method, 1 mark for correct answer.

10. Answer: 729 cm³

Working: Volume = Edge × Edge × Edge = 9 cm × 9 cm × 9 cm = 729 cm³.
Concept: The volume of a cube is found by cubing the edge length.
Marking: 1 mark for correct method, 1 mark for correct answer.

11. Answer: 30 litres

Working: Volume in cm³ = 50 cm × 30 cm × 20 cm = 30 000 cm³. Volume in litres = 30 000 cm³ ÷ 1000 cm³/litre = 30 litres.
Concept: 1 litre = 1000 cm³. To convert from cm³ to litres, divide by 1000.
Marking: 1 mark for correct volume in cm³, 1 mark for correct conversion to litres.

12. Answer: 7 cm

Working: Height = Volume ÷ Base Area = 343 cm³ ÷ 49 cm² = 7 cm.
Concept: The volume of a cuboid is Base Area × Height. Therefore, Height = Volume ÷ Base Area.
Marking: 1 mark for correct method, 1 mark for correct answer.

13. Answer: 40 cm

Working: Volume of water in first tank = 60 cm × 40 cm × 25 cm = 60 000 cm³. Height in second tank = Volume ÷ (Length × Width) = 60 000 cm³ ÷ (50 cm × 30 cm) = 60 000 cm³ ÷ 1500 cm² = 40 cm.
Concept: The volume of water remains the same when poured into another tank. Use the new base area to find the new height.
Marking: 1 mark for correct volume, 1 mark for correct height.

14. Answer: 1200 cm³

Working: Volume = Length × Width × Height = 15 cm × 10 cm × 8 cm = 1200 cm³.
Concept: The volume of a cuboid is found by multiplying its length, width, and height.
Marking: 1 mark for correct method, 1 mark for correct answer.

15. Answer: 6 cm

Working: Edge length = ∛216 cm³ = 6 cm.
Concept: The volume of a cube is edge³. To find the edge length from the volume, find the cube root. 6 × 6 × 6 = 216.
Marking: 1 mark for correct method, 1 mark for correct answer.

Section C: Problem-Solving Questions (Questions 16 to 20)

(4 marks each)

16. Answer (a): 36 000 cm³ Answer (b): 24 000 cm³

Working:
- (a) Total volume of tank = 50 cm × 40 cm × 30 cm = 60 000 cm³. Volume of water = (3/5) × 60 000 cm³ = 36 000 cm³.
- (b) Volume needed = Total volume - Volume of water = 60 000 cm³ - 36 000 cm³ = 24 000 cm³.
Concept: To find a fraction of a volume, multiply the total volume by the fraction. The remaining volume is the total minus the filled part.
Marking: (a) 1 mark for total volume, 1 mark for water volume. (b) 1 mark for correct method, 1 mark for correct answer.

17. Answer (a): 16 000 cm³ Answer (b): 25.2 cm (or 25 cm if using cube root of 16000)

Working:
- (a) Volume of cube = Volume of water displaced = Length × Width × Rise in water level = 80 cm × 50 cm × 4 cm = 16 000 cm³.
- (b) Edge length = ∛16 000 cm³. Since 25³ = 15 625 and 26³ = 17 576, the edge length is approximately 25.2 cm. (Note: For P6, they may be expected to leave it as ∛16 000 or give a decimal approximation. The exact cube root is not a whole number.)
Concept: When an object is submerged, it displaces a volume of water equal to its own volume. The displaced water volume is calculated as the base area of the tank multiplied by the rise in water level.
Marking: (a) 1 mark for correct method, 1 mark for correct answer. (b) 1 mark for correct method, 1 mark for correct answer (accept ∛16 000 or 25.2 cm).

18. Answer (a): 24 000 cm³ Answer (b): 33 minutes

Working:
- (a) Total volume = 60 cm × 40 cm × 35 cm = 84 000 cm³. Initial water volume = (2/7) × 84 000 cm³ = 24 000 cm³.
- (b) Volume needed to fill = 84 000 cm³ - 24 000 cm³ = 60 000 cm³. Rate = 2 litres/min = 2000 cm³/min. Time = 60 000 cm³ ÷ 2000 cm³/min = 30 minutes.
Concept: Find the remaining volume to be filled. Ensure units are consistent (convert litres to cm³). Time = Volume ÷ Rate.
Marking: (a) 1 mark for total volume, 1 mark for initial water volume. (b) 1 mark for remaining volume and conversion, 1 mark for correct time.

19. Answer (a): 81 000 cm³ Answer (b): 81 containers

Working:
- (a) Drop in water level = 40 cm - 25 cm = 15 cm. Volume poured out = 90 cm × 60 cm × 15 cm = 81 000 cm³.
- (b) Volume of one cubical container = 10 cm × 10 cm × 10 cm = 1000 cm³. Number of containers = 81 000 cm³ ÷ 1000 cm³ = 81.
Concept: The volume of water poured out is the volume of the "slice" of water removed. Then divide the total volume by the volume of one container.
Marking: (a) 1 mark for drop in water level, 1 mark for volume. (b) 1 mark for volume of one container, 1 mark for correct number of containers.

20. Answer (a): 225 000 cm³ Answer (b): 38 cm

Working:
- (a) Total volume = 100 cm × 60 cm × 50 cm = 300 000 cm³. Initial water volume = (3/4) × 300 000 cm³ = 225 000 cm³.
- (b) Volume of metal cuboid = 20 cm × 15 cm × 10 cm = 3000 cm³. New total volume of water + cuboid = 225 000 cm³ + 3000 cm³ = 228 000 cm³. New water level height = New volume ÷ Base area of tank = 228 000 cm³ ÷ (100 cm × 60 cm) = 228 000 cm³ ÷ 6000 cm² = 38 cm.
Concept: When an object is submerged, the water level rises because the object takes up space. The new total volume (water + object) divided by the base area gives the new height.
Marking: (a) 1 mark for total volume, 1 mark for initial water volume. (b) 1 mark for volume of cuboid and new total volume, 1 mark for correct new height.