A rectangular storage container has a height of 18 units. The base of the container is a rectangle with a...

1. TRANSLATE the problem information

• Given information:
  • Height of container: 18 units
  • Width of base: 8 units
  • Volume of container: 2,304 cubic units
  • Need to find: length of base

• This is asking us to work backwards from volume to find a missing dimension.

2. TRANSLATE the volume relationship

• For any rectangular container (rectangular prism):
  \(\mathrm{Volume = length × width × height}\)

• Substituting our known values:
  \(\mathrm{2,304 = length × 8 × 18}\)

3. SIMPLIFY to solve for length

• First, multiply the known dimensions:
  \(\mathrm{8 × 18 = 144}\)

• So our equation becomes:
  \(\mathrm{2,304 = length × 144}\)

• Divide both sides by 144:
  \(\mathrm{length = 2,304 ÷ 144 = 16}\)

4. Verify the answer

• Check: \(\mathrm{16 × 8 × 18 = 2,304}\) ✓

Answer: 16

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make calculation errors, especially in the division step 2,304 ÷ 144.

Some students might incorrectly calculate this division, perhaps getting confused by the larger numbers or making basic arithmetic mistakes. For instance, they might get 14 or 18 instead of 16, leading to an incorrect final answer.

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which dimension they're solving for or confuse the setup of the volume formula.

Some students might incorrectly set up the equation by mixing up width and length, or they might forget that volume involves all three dimensions. This confusion in the initial setup means their entire solution process will be wrong from the start.

The Bottom Line:

This problem requires careful attention to both the initial setup and the final calculation. Success comes from methodically identifying what you know, what you need to find, and systematically working through the algebra without rushing the arithmetic.