Maria is ordering pizza for a school event. A circular pizza has a diameter of 12 inches. What is the...

1. TRANSLATE the problem information

• Given information:
  • Circular pizza with diameter = 12 inches
  • Need to find the area in square inches

2. INFER the approach needed

• The area formula for a circle is \(\mathrm{A = πr^2}\)
• Problem gives diameter, but formula needs radius
• Key insight: Must find radius first using \(\mathrm{r = diameter ÷ 2}\)

3. Calculate the radius

• Radius = diameter ÷ 2 = \(\mathrm{12 ÷ 2 = 6}\) inches

4. SIMPLIFY using the area formula

• Substitute radius into \(\mathrm{A = πr^2}\)
• \(\mathrm{A = π(6)^2}\)
• \(\mathrm{A = π(36)}\)
• \(\mathrm{A = 36π}\) square inches

Answer: C. \(\mathrm{36π}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students jump directly to using the area formula without recognizing they need to convert diameter to radius first.

They see "diameter = 12" and immediately substitute into \(\mathrm{A = πr^2}\):

\(\mathrm{A = π(12)^2 = 144π}\)

This fundamental oversight - not recognizing that \(\mathrm{diameter ≠ radius}\) - is the most dangerous error because it feels mathematically correct.

This may lead them to select Choice D (\(\mathrm{144π}\)).

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly find \(\mathrm{radius = 6}\), but forget to square it in the area formula.

They calculate \(\mathrm{A = πr}\) as \(\mathrm{A = π(6) = 6π}\) instead of \(\mathrm{A = πr^2 = π(6)^2 = 36π}\). This happens when students rush through the exponent or confuse area formula with circumference formula.

This may lead them to select Choice A (\(\mathrm{6π}\)).

The Bottom Line:

This problem tests whether students can bridge the gap between what's given (diameter) and what's needed (radius) for the area formula. Success requires careful attention to the relationship between diameter and radius, plus precise execution of the squaring step.