Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

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In a new sprinkler system that sprays 20 meters farther than the old one, what is the circumference of the spraying area of the new system?

  1. 314.2 meters

  2. 439.6 meters

  3. 628.3 meters

  4. 785.4 meters

The correct answer is: 439.6 meters

To determine the circumference of the spraying area of the new sprinkler system, we first need to calculate the radius of the new system. The new system sprays 20 meters farther than the old one, so if we assume the old system had a radius of 'r' meters, the new system's radius becomes 'r + 20' meters. The formula for the circumference of a circle is given by \( C = 2\pi r \), where \( r \) is the radius. For the new system, substituting the new radius into the formula gives us: \[ C = 2\pi (r + 20) \] To calculate the circumference, we need the specific radius 'r' of the old system, which isn't provided directly in the question. However, the answer choice provided, which suggests 439.6 meters, implies that the relevant calculations producing this circumference based on a realistic radius of the old system would be effective. For instance, if we calculate the circumference with \( r + 20 \) resulting in 439.6 meters, you can work backward to find the equivalent value of 'r' that makes this true. Rearranging the circumference equation gives: \[ r + 20 = \frac

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