A right circular cylinder has a height of 8 meters (m) and a base with a radius of 12 m....

1. TRANSLATE the problem information

• Given information:
  • Height of cylinder: 8 meters
  • Radius of base: 12 meters
  • Need to find: Volume in m³

2. INFER the approach

• This is a cylinder volume problem, so we need the formula \(\mathrm{V = \pi r^2h}\)
• We have both radius and height, so we can substitute directly

3. SIMPLIFY the calculation

• Substitute the values: \(\mathrm{V = \pi(12)^2(8)}\)
• Calculate the exponent: \(\mathrm{12^2 = 144}\)
• Multiply: \(\mathrm{V = \pi(144)(8) = 1,152\pi}\)

Answer: D. \(\mathrm{1,152\pi}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make calculation errors when squaring the radius or performing the final multiplication.

For example, they might calculate \(\mathrm{12^2}\) as 24 instead of \(\mathrm{144}\), or make errors in multiplying \(\mathrm{144 \times 8}\). This leads to selecting an incorrect answer choice or getting confused about which option matches their result.

Second Most Common Error:

Poor TRANSLATE reasoning: Students accidentally switch the radius and height values in their calculation.

They might use \(\mathrm{V = \pi(8)^2(12)}\) instead of \(\mathrm{V = \pi(12)^2(8)}\), which gives \(\mathrm{V = \pi(64)(12) = 768\pi}\). This may lead them to select Choice C (\(\mathrm{768\pi}\)).

The Bottom Line:

This problem tests whether students can accurately recall and apply the cylinder volume formula while maintaining precision in their arithmetic calculations.