A circle has a radius of 43 meters. What is the area, in square meters, of the circle?

1. TRANSLATE the problem information

• Given information:
  • Circle has \(\mathrm{radius = 43\text{ meters}}\)
  • Need to find: area in square meters

2. TRANSLATE to mathematical setup

• Since we need area of a circle, use the area formula: \(\mathrm{A = \pi r^2}\)
• Substitute the given radius: \(\mathrm{A = \pi(43)^2}\)

3. SIMPLIFY the calculation

• Calculate the square: \(\mathrm{43^2 = 1849}\) (use calculator if needed)
• Therefore: \(\mathrm{A = \pi(1849) = 1849\pi}\) square meters

Answer: D. \(\mathrm{1849\pi}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Confusing area formula with circumference formula

Students may recall that circles involve "π times something with the radius," but mix up the formulas. They might use \(\mathrm{C = 2\pi r}\) instead of \(\mathrm{A = \pi r^2}\), calculating \(\mathrm{2\pi(43) = 86\pi}\).

This leads them to select Choice C (\(\mathrm{86\pi}\)).

Second Most Common Error:

Poor SIMPLIFY execution: Using area formula correctly but forgetting to square the radius

Students set up \(\mathrm{A = \pi r^2}\) correctly but then substitute as \(\mathrm{A = \pi(43)}\) instead of \(\mathrm{A = \pi(43)^2}\), essentially treating it like \(\mathrm{A = \pi r}\).

This leads them to select Choice B (\(\mathrm{43\pi}\)).

The Bottom Line:

This problem tests whether students can distinguish between area and circumference formulas for circles. The calculation itself is straightforward once the correct formula is applied, but formula confusion is the primary challenge.