A play train travels around a clock tower in a circle. The radius of the train track measures 8 feet. What is the distance that the train travels around the track once? Use 3.14 fo... A play train travels around a clock tower in a circle. The radius of the train track measures 8 feet. What is the distance that the train travels around the track once? Use 3.14 for π.
Understand the Problem
The question is asking for the circumference of a circle, which is calculated using the formula C = 2πr. Given the radius of 8 feet, we will apply the formula to find the distance the train travels around the track once, using π as 3.14.
Answer
The distance that the train travels around the track once is $50.24$ ft.
Answer for screen readers
The distance that the train travels around the track once is $50.24$ ft.
Steps to Solve
- Identify the formula for circumference
To find the circumference $C$ of a circle, we use the formula:
$$ C = 2 \pi r $$
where $r$ is the radius and $\pi$ is approximately 3.14.
- Plug in the values
Given that the radius $r = 8$ feet, substitute this value into the formula:
$$ C = 2 \times 3.14 \times 8 $$
- Calculate the circumference
First, calculate $2 \times 3.14$:
$$ 2 \times 3.14 = 6.28 $$
Now substitute this back into the equation:
$$ C = 6.28 \times 8 $$
Next, perform the multiplication:
$$ C = 50.24 $$
Thus, the circumference of the circle is 50.24 feet.
The distance that the train travels around the track once is $50.24$ ft.
More Information
The circumference is the total distance around a circle and is important in various applications such as calculating the length of fencing needed for circular areas or the distance traveled by objects in circular motion.
Tips
- Confusing diameter with radius: Always ensure you're using the radius in your calculations, as the formula depends specifically on this measurement.
- Miscalculating $\pi$: Make sure to use the correct value for $\pi$, which in this case is 3.14.
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