A storage tank is designed in the shape of a right circular cylinder with a height of 20 centimeters and...

1. TRANSLATE the problem information

• Given information:
  • Right circular cylinder with \(\mathrm{height = 20\ cm}\)
  • Base \(\mathrm{radius = 3\ cm}\)
  • \(\mathrm{Volume = k\pi}\) cubic centimeters (need to find k)

2. INFER the approach needed

• Since we need volume and have radius and height, use the cylinder volume formula
• The volume will be expressed in terms of π, so we can find k by comparing

3. SIMPLIFY using the cylinder volume formula

• Volume formula: \(\mathrm{V = \pi r^2h}\)
• Substitute: \(\mathrm{V = \pi(3)^2(20)}\)
• Calculate:
  \(\mathrm{V = \pi(9)(20)}\)
  \(\mathrm{V = 180\pi}\) cubic centimeters

4. INFER the final answer

• Since \(\mathrm{volume = k\pi}\) and we found \(\mathrm{volume = 180\pi}\)
• Therefore: \(\mathrm{k = 180}\)

Answer: C) 180

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students forget to square the radius when substituting into the formula.

They might calculate \(\mathrm{V = \pi(3)(20) = 60\pi}\) instead of \(\mathrm{V = \pi(3)^2(20) = 180\pi}\).

This leads them to select Choice A (60).

Second Most Common Error:

Missing conceptual knowledge: Students confuse volume formulas and might try to use surface area or other geometric formulas instead of \(\mathrm{V = \pi r^2h}\).

This causes confusion and leads to guessing among the answer choices.

The Bottom Line:

This problem tests whether students can accurately apply a memorized formula with careful attention to exponents - the kind of precision that separates solid algebra skills from careless execution.