A rectangular fish tank has a volume of 4{,080} cubic inches. The base of the tank has a length of...

1. TRANSLATE the problem information

• Given information:
  • Volume of fish tank = 4,080 cubic inches
  • Length of base = 24 inches
  • Width of base = 10 inches
  • Find: height of tank

2. INFER the approach needed

• Since we have a rectangular fish tank, we're working with a rectangular prism
• We know volume and two dimensions, need to find the third dimension
• We'll use the volume formula and solve for height

3. SIMPLIFY using the volume formula

• Volume = length × width × height
• Substitute known values: \(\mathrm{4,080 = 24 \times 10 \times h}\)
• Multiply the base dimensions: \(\mathrm{4,080 = 240 \times h}\)
• Solve for height: \(\mathrm{h = 4,080 \div 240 = 17}\)

Answer: C) 17

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor TRANSLATE reasoning: Students may confuse which measurement represents which dimension, or misread the volume units versus the length units.

Some students might try to add the dimensions instead of multiplying them, or incorrectly set up the equation by mixing up which values go where. This leads to confusion and random guessing among the answer choices.

Second Most Common Error:

Weak SIMPLIFY execution: Students correctly set up \(\mathrm{4,080 = 240 \times h}\) but make arithmetic errors when dividing 4,080 by 240.

Common calculation mistakes include getting 16 instead of 17, which may lead them to select Choice B (16), or other computational errors that result in selecting Choice A (15) or Choice C (18).

The Bottom Line:

This is fundamentally a straightforward "plug into formula and solve" problem, but students can stumble on the basic setup or the final division step. Success depends on recognizing the rectangular prism connection and executing the arithmetic accurately.