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St Nicholas 2025 P6 Maths Prelim — Paper 2 Q10 Solution

Paper 2 · Q10 · 3 marks · Volume of Cube and Cuboid

Question

X and Y are two rectangular tanks. At first, X was filled with some water and Y was empty. The base area of Y is 135 cm^2. Some water was poured from X to Y without spilling. In the end, the amount of water in Y was 2430 cm^3. The height of water in X was $\frac{3}{4}$ the height of water in Y. The amount of water then left in X was $\frac{2}{3}$ the amount of water in Y. What is the base area of X?
Answer: 120 cm^2

Worked solution

  1. Height of water in Y $= 2430 \div 135 = 18\text{ cm}$. Height of water in X $= \frac{3}{4} \times 18 = 13.5\text{ cm}$. Volume of water in X $= \frac{2}{3} \times 2430 = 1620\text{ cm}^3$. Base area of X $= 1620 \div 13.5 = 120\text{ cm}^2$.

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