A rectangular aquarium has a base with an area of 800 square centimeters. The aquarium contains water to a height...

1. TRANSLATE the problem information

• Given information:
  • Base area of aquarium = \(800 \text{ cm}^2\)
  • Water height before stones = \(30 \text{ cm}\)
  • Water height after stones = \(32.5 \text{ cm}\)
  • Need to find: volume of stones

2. INFER the physical relationship

• When objects are submerged in water, they displace their volume in water
• This displacement causes the water level to rise
• Therefore: volume of stones = volume of displaced water

3. TRANSLATE to find the key measurement

• The displaced water height = change in water level
• Height change = \(32.5 \text{ cm} - 30 \text{ cm} = 2.5 \text{ cm}\)

4. Calculate the volume using the rectangular prism formula

• The displaced water forms a rectangular prism with:
  • Base area = \(800 \text{ cm}^2\) (same as aquarium)
  • Height = \(2.5 \text{ cm}\) (the rise in water level)
• Volume of stones = \(800 \text{ cm}^2 \times 2.5 \text{ cm} = 2000 \text{ cm}^3\)

Answer: B) 2000

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize the displacement principle and instead try to calculate the total water volume or use the absolute height measurements directly.

They might calculate \(800 \times 30 = 24,000 \text{ cm}^3\) or \(800 \times 32.5 = 26,000 \text{ cm}^3\), both of which are far larger than any answer choice. This leads to confusion and guessing.

Second Most Common Error:

Poor TRANSLATE reasoning: Students understand the displacement concept but use the wrong height measurement in their calculation.

For example, they might round the height change from \(2.5 \text{ cm}\) to \(2.0 \text{ cm}\) for easier calculation, leading to \(800 \times 2 = 1600 \text{ cm}^3\). This may lead them to select Choice A (1600).

The Bottom Line:

This problem tests whether students can connect the physical concept of displacement to the mathematical calculation of volume change. The key insight is recognizing that you need the change in water level, not the absolute water levels.