Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

What is the circumference of the spraying area when a new sprinkler system sprays 20 meters farther than the old system?

1. 314.2 meters

2. 439.6 meters

3. 125.6 meters

4. 404.7 meters

The correct answer is: 439.6 meters

To find the circumference of the spraying area for the new sprinkler system, we first need to understand that the circumference of a circle is calculated using the formula \( C = 2\pi r \), where \( r \) is the radius. Assuming the old sprinkler system has a spraying radius of \( r \) meters, the new system sprays 20 meters farther, giving it a new radius of \( r + 20 \) meters. To find the circumference of the new spraying area, we substitute the new radius into the circumference formula: \[ C = 2\pi(r + 20) \] This can be simplified to: \[ C = 2\pi r + 40\pi \] To determine the exact value, we would need the original radius \( r \). However, if we assume that \( r \) represents a certain baseline (for example, if \( r \) were 0, resulting in a circumference of just the additional segment from the increased radius), the crucial part here is recognizing that the larger radius directly contributes to the circumference increase. If we test the provided numerical options for reasonable values for \( r \): - Say, if the old system’s radius were approximately 10