A right circular cylinder has a base diameter of 22 centimeters and a height of 6 centimeters. What is the...

1. TRANSLATE the problem information

• Given information:
  • Right circular cylinder
  • Base diameter = 22 cm
  • Height = 6 cm
• Need to find: Volume in cubic centimeters

2. INFER the approach needed

• Volume formula for a cylinder is \(\mathrm{V = πr^2h}\)
• The formula requires radius (r), but we're given diameter
• Strategy: First convert diameter to radius, then apply the formula

3. TRANSLATE diameter to radius

• Radius = diameter ÷ 2
• \(\mathrm{r = 22 ÷ 2 = 11\ cm}\)

4. SIMPLIFY by substituting into the volume formula

• \(\mathrm{V = πr^2h}\)
• \(\mathrm{V = π(11)^2(6)}\)
• \(\mathrm{V = π(121)(6)}\)
• \(\mathrm{V = 726π}\) cubic centimeters

Answer: C. \(\mathrm{726π}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about radius vs diameter: Students might use the diameter directly in the volume formula instead of converting to radius first.

If they substitute \(\mathrm{V = π(22)^2(6)}\), they get \(\mathrm{V = π(484)(6) = 2,904π}\), leading them to select Choice D (\(\mathrm{2,904π}\)).

Second Most Common Error:

Weak SIMPLIFY execution: Students make arithmetic errors when calculating \(\mathrm{π(11)^2(6)}\).

Common mistakes include:

• Incorrectly calculating \(\mathrm{11^2}\) (getting something other than 121)
• Errors in multiplying \(\mathrm{121 × 6}\)

These calculation errors can lead to selecting wrong answer choices or confusion and guessing.

The Bottom Line:

This problem tests whether students truly understand that radius and diameter are different measurements, and whether they can systematically apply the cylinder volume formula with accurate arithmetic.