The volume of a right rectangular prism is 119 cubic centimeters. The area of the base of the prism is...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{Volume = 119\text{ cubic centimeters}}\)
  • \(\mathrm{Base\text{ }Area = 17\text{ square centimeters}}\)
• Need to find: height of the prism

2. INFER the appropriate formula and strategy

• For a right rectangular prism: \(\mathrm{Volume = Base\text{ }Area \times Height}\)
• Since we have volume and base area, we can solve for height
• Strategy: Rearrange the formula to isolate height

3. SIMPLIFY by rearranging and calculating

• Start with: \(\mathrm{119 = 17 \times Height}\)
• Divide both sides by 17: \(\mathrm{Height = 119 \div 17}\)
• Calculate: \(\mathrm{Height = 7\text{ centimeters}}\)

4. Verify the answer

• Check: \(\mathrm{17 \times 7 = 119}\) ✓

Answer: B) 7

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about volume formulas: Students might try to use \(\mathrm{V = l \times w \times h}\) instead of recognizing that the base area is already provided as one combined measurement.

They might think: "I need length, width, and height, but I only have volume and one area measurement." This leads to confusion about what information is actually available and causes them to get stuck or guess randomly.

Second Most Common Error:

Weak SIMPLIFY execution: Students make arithmetic errors when dividing 119 by 17, potentially calculating \(\mathrm{119 \div 17}\) incorrectly.

Common miscalculations might give results like 6, 8, or other values from the answer choices. This may lead them to select Choice A (6) or Choice C (8) based on their incorrect arithmetic.

The Bottom Line:

This problem tests whether students can recognize when they have sufficient information in a different form than expected (base area instead of separate length and width) and apply the volume formula correctly.