A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{Volume} = 432\) cubic centimeters
  • \(\mathrm{Area\,of\,base} = 24\) square centimeters
  • Find: height in centimeters
• What this tells us: We have two key pieces needed for the volume formula

2. INFER the solution approach

• Since we have volume and base area, we can use the cylinder volume formula directly
• Key insight: \(\mathrm{V} = \pi\mathrm{r}^2\mathrm{h}\), and \(\pi\mathrm{r}^2\) is exactly the area of the base
• So the formula becomes: \(\mathrm{V} = (\mathrm{Area\,of\,base}) \times \mathrm{h}\)

3. TRANSLATE the formula with our values

• Substitute known values: \(432 = 24 \times \mathrm{h}\)

4. SIMPLIFY to solve for height

• Divide both sides by 24: \(\mathrm{h} = 432 \div 24\)
• Calculate: \(\mathrm{h} = 18\)

Answer: A. 18

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that \(\pi\mathrm{r}^2\) in the volume formula equals the area of the base that's already given. Instead, they try to find the radius first by solving \(\pi\mathrm{r}^2 = 24\), then attempt to use \(\mathrm{V} = \pi\mathrm{r}^2\mathrm{h}\). This creates unnecessary complexity with π calculations and potential rounding errors.

This approach might lead them to get confused with decimal approximations and select Choice C (216) or abandon the systematic solution and guess.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misread what they're solving for and confuse the area of the base (24) with the height, leading them to select Choice B (24) without performing any calculations.

The Bottom Line:

The key insight is recognizing that you don't need to find the radius separately - the area of the base is already provided and can substitute directly into the volume formula. This transforms a potentially complex problem into simple division.