A circle has a radius of 11 centimeters. Which expression gives the area, in cm^2, of the circle?

1. TRANSLATE the problem information

• Given information:
  • Circle has radius = 11 centimeters
  • Need to find: area of the circle in cm²

2. INFER the approach

• Since we need the area of a circle, we must use the area formula: \(\mathrm{A = \pi r^2}\)
• We have the radius, so we can substitute directly into the formula

3. Apply the formula

• Substitute \(\mathrm{r = 11}\) into \(\mathrm{A = \pi r^2}\):
  \(\mathrm{A = \pi(11)^2}\)
  \(\mathrm{A = \pi \cdot 11^2}\)
• Looking at the answer choices, this matches choice (C)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion: Mixing up area and circumference formulas
Students remember that circles involve π and radius, but grab the wrong formula. They use \(\mathrm{C = 2\pi r}\) instead of \(\mathrm{A = \pi r^2}\), thinking "circles use 2π times radius." This leads them to select Choice A (\(\mathrm{2\pi \cdot 11}\)).

Second Most Common Error:

Weak INFER skill: Using the correct area formula but forgetting to square the radius
Students know they need \(\mathrm{A = \pi r^2}\) but mentally skip the squaring step, calculating \(\mathrm{A = \pi \cdot r}\) instead. This incomplete application of the formula leads them to select Choice B (\(\mathrm{\pi \cdot 11}\)).

The Bottom Line:

This problem tests whether students can distinguish between area and circumference formulas for circles, and whether they can correctly apply the area formula by squaring the radius.