A circular pond has a radius of 10 meters. What is the area, in square meters, of the pond? (Use...

1. TRANSLATE the problem information

• Given information:
  • Circular pond with radius = 10 meters
  • \(\mathrm{\pi = 3.14}\)
  • Need to find: area in square meters

2. INFER the appropriate formula

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

3. SIMPLIFY by substituting and calculating

• \(\mathrm{A = \pi r^2 = 3.14 \times 10^2}\)
• First calculate the radius squared: \(\mathrm{10^2 = 100}\)
• Then multiply: \(\mathrm{A = 3.14 \times 100 = 314}\) square meters

Answer: C (314)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion: Mixing up area and circumference formulas

Students sometimes remember 'circle problems use \(\mathrm{\pi r}\)' but forget whether it's \(\mathrm{\pi r^2}\) (area) or \(\mathrm{2\pi r}\) (circumference). Using the circumference formula: \(\mathrm{C = 2\pi r = 2 \times 3.14 \times 10 = 62.8}\), they round to get approximately 63.

This may lead them to select Choice B (63)

Second Most Common Error:

Weak SIMPLIFY execution: Forgetting to square the radius

Students correctly identify the area formula \(\mathrm{A = \pi r^2}\) but then substitute incorrectly as \(\mathrm{A = \pi \times r}\) instead of \(\mathrm{A = \pi \times r^2}\). This gives: \(\mathrm{A = 3.14 \times 10 = 31.4}\), which rounds to 31.

This may lead them to select Choice A (31)

The Bottom Line:

Circle area problems require both knowing the correct formula (\(\mathrm{A = \pi r^2}\)) AND carefully executing the arithmetic with the squared radius. The wrong answer choices are specifically designed to catch these two most common mistakes.