A rectangular glass aquarium containing decorative rocks is filled to the top with water before fish are added. The aquarium...

1. TRANSLATE the problem setup

• Given information:
  • Aquarium dimensions: 22 cm long, 20 cm wide, 4 cm high
  • Contains decorative rocks
  • Needs 240 cm³ of water to fill to the top

• What this tells us: The rocks are taking up space, leaving only 240 cm³ for water

2. INFER the solution strategy

• Key insight: If the aquarium needs only 240 cm³ to fill completely, the rocks must be occupying the rest of the space
• Strategy: Find total volume, then subtract the water volume to get rock volume

3. SIMPLIFY the total volume calculation

• Total volume = length × width × height
• V = \(22 \times 20 \times 4 = 1,760 \text{ cm}^3\) (use calculator)

4. SIMPLIFY the final calculation

• Volume of rocks = Total volume - Water volume
• Volume of rocks = \(1,760 - 240 = 1,520 \text{ cm}^3\)

Answer: C) \(1520 \text{ cm}^3\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what the 240 cm³ represents. They might think it's the volume of the rocks rather than the remaining space for water.

This leads them to calculate: Total volume = \(22 \times 20 \times 4 = 1,760 \text{ cm}^3\), then assume the rocks are 240 cm³, selecting Choice A (\(240 \text{ cm}^3\)) or getting confused about what to do next.

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly find the total volume as 1,760 cm³ but then think this IS the answer for rock volume, not recognizing they need to subtract the water volume.

This may lead them to select Choice D (\(1760 \text{ cm}^3\)).

The Bottom Line:

The key challenge is understanding the relationship between the three volumes: total aquarium volume, water volume, and rock volume. Students must recognize that the water fills only the "leftover" space not occupied by rocks.