To solve this problem, we need to calculate the circumference of the circular dirt course and then multiply that by the number of laps Fiona takes to find the total distance covered. Here's the step-by-step solution:
Step 1: Calculate the circumference of the circular course.
The formula for the circumference (C) of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159.
Step 2: Plug the values into the formula.
The radius of the circular course is given as 70 meters. Hence, the circumference [tex]\( C \)[/tex] can be calculated as follows:
[tex]\[ C = 2 \times \pi \times 70 \][/tex]
[tex]\[ C = 140\pi \][/tex]
[tex]\[ C \approx 140 \times 3.14159 \][/tex]
[tex]\[ C \approx 439.822 \][/tex]
Step 3: Determine the total distance covered in two laps.
Fiona completes two laps around the course, so the total distance (D) covered is twice the circumference. Therefore:
[tex]\[ D = 2 \times C \][/tex]
[tex]\[ D \approx 2 \times 439.822 \][/tex]
[tex]\[ D \approx 879.644 \][/tex]
Step 4: Approximate the answer to match the options given in the question.
The result should be rounded to match the options provided in the question:
[tex]\[ D \approx 879.6 \][/tex]
Step 5: Choose the correct answer from the provided options.
The closest answer to our calculation is about 879.6 meters, which is not listed exactly as such among the choices provided. However, it's clear that the correct answer is:
C. about 879.2 meters
The slight difference in the last decimal place is due to the level of precision used in approximating pi. To better match one of the given options, we can round our answer. 879.6 meters, when rounded to one decimal place, is 879.6 meters, which is not provided, the closest listed option being about 879.2 meters.
