Geometry Circumference Calculation: TEAS Practice Question with Answer & Explanation

Understanding Circumference in Geometry

In this problem, you are asked to find the length of a "trim" or "barrier" that goes around the outside of a circle. In geometry, the distance around the outside of a circle is known as the circumference.

The Formula

To find the circumference ($C$), you need to know either the radius ($r$) or the diameter ($d$). The problem states that the distance from the center to the edge is 10 inches. This distance is defined as the radius.

The formula for circumference using the radius is: $$C = 2 \pi r$$

Step-by-Step Calculation

1. Identify the variables: $r = 10$; $\pi \approx 3.14$.
2. Plug values into the formula: $C = 2 \times 3.14 \times 10$.
3. Multiply the constants: $2 \times 3.14 = 6.28$.
4. Complete the multiplication: $6.28 \times 10 = 62.8$.

The total length of the metal trim needed is 62.8 inches.

Analysis of Incorrect Answers

• Choice A (31.4 inches): This result comes from forgetting the "$2$" in the formula $2 \pi r$ (calculating $\pi \times r$ instead). This is a common error when students confuse the radius for the diameter.
• Choice C (78.5 inches): This result comes from mistakenly using the area formula ($A = \pi r^2$) and dividing by something else, or using a radius of 5 with an incorrect formula. It does not represent the outer boundary.
• Choice D (314.0 inches): This result is the Area of the circle ($\pi r^2 = 3.14 \times 10^2 = 314$). On the TEAS, always check if the question asks for the space inside (area) or the distance around (circumference).

TEAS Math Tip: Keywords

When reading TEAS geometry word problems, look for these keywords to determine which formula to use:

• Circumference/Perimeter: perimeter, edge, trim, fence, boundary, "around the outside."
• Area: surface, rug, paint, "covering the space inside," square units.

Remember: Diameter is twice the radius ($d = 2r$). If the problem gives you the diameter, you can simply use $C = \pi d$.