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P6 Volume Questions (with Worked Solutions)
Volume of cubes, cuboids, and liquids — P6 prelim practice. Every question is from a real Singapore P6 preliminary exam, marked instantly, with step-by-step solutions.
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Example Volume questions
A few real volume questions from P6 prelim papers. The full set — with marking and progress tracking — is inside SG Maths Exam.
Nanyang 2025 · Paper 2 · Q11(b) · 3 marks
Tank G is $\frac{3}{5}$ full of water. After all the water from Tank H is poured into Tank G, Tank G is then $\frac{7}{10}$ full of water. The base area of Tank G is 5000 cm^2. Find the height of Tank G.
Worked solution
- The water poured in from Tank H is $11\,250\text{ cm}^3$, which raised Tank G from $\frac{3}{5}$ to $\frac{7}{10}$ full. The increase $= \frac{7}{10} - \frac{3}{5} = \frac{7}{10} - \frac{6}{10} = \frac{1}{10}$ of Tank G. So $\frac{1}{10}$ of the capacity $= 11\,250\text{ cm}^3$, capacity $= 112\,500\text{ cm}^3$. Height $= 112\,500 \div 5000 = 22.5$ cm.
Nanyang 2025 · Paper 2 · Q12(b) · 3 marks
Lilian dipped the cube into a pail of paint. She then separated the cube back into the nine original wooden cuboids. Find the total unpainted area of the nine wooden cuboids.
Worked solution
- Total surface area of all 9 cuboids: each cuboid is $18 \times 18 \times 2 = 648$, so each cuboid measures $18\text{ cm} \times 18\text{ cm} \times 2\text{ cm}$. Surface area of one cuboid $= 2(18 \times 18 + 18 \times 2 + 18 \times 2) = 2(324 + 36 + 36) = 792\text{ cm}^2$. Total for 9 cuboids $= 9 \times 792 = 7128\text{ cm}^2$. The painted area is the cube's outer surface $= 6 \times 18 \times 18 = 1944\text{ cm}^2$. But internal painted surfaces appear when separated
- total painted $= 7128 - 2592$. Unpainted area $= 2592\text{ cm}^2$.
St Nicholas 2025 · Paper 2 · Q13(b) · 2 marks
For the fish tank, (b) At the end of 25 minutes, what fraction of the tank was not filled with water?
Worked solution
- $\frac{3}{8}$ of the tank $= 48\text{ l}$, so $\frac{1}{8} = 16\text{ l}$ and the full tank $= 8 \times 16 = 128\text{ l}$. After 25 minutes the tank held 108 l, so $128 - 108 = 20\text{ l}$ was empty. Fraction not filled $= \frac{20}{128} = \frac{5}{32}$.
St Nicholas 2025 · Paper 2 · Q13(c) · 1 mark
For the fish tank, (c) The tap was turned on again at the same rate as before. How many more minutes did it take to fill the tank completely?
Worked solution
- Water still needed $= 20\text{ l}$. At $2.4\text{ l per minute}$, time $= 20 \div 2.4 = 8\frac{1}{3}\text{ min}$.
Nanyang 2025 · Paper 2 · Q11(a) · 1 mark
Tank G and Tank H are rectangular containers. Tank H measures 40 cm long, 30 cm wide and 15 cm high. Tank H is $\frac{5}{8}$ full of water. What is the volume of water in Tank H?
Worked solution
- Capacity of Tank H $= 40 \times 30 \times 15 = 18\,000\text{ cm}^3$. Volume of water $= \frac{5}{8} \times 18\,000 = 11\,250\text{ cm}^3$.
Raffles Girls 2025 · Paper 1 Booklet B · Q25(b) · 1 mark
Find the greatest number of cubes that can be added to the solid without changing the front view and the side view.
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