The diameter of a circle measures 20 ft. What is the circumference of the circle?
Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
The Correct Answer and Explanation is:
To find the circumference of a circle when the diameter is given, you can use the formula:
[
\text{Circumference} = \pi \times \text{Diameter}
]
In this case, the diameter of the circle is given as 20 feet. Substituting this value into the formula and using ( \pi ) as 3.14:
[
\text{Circumference} = 3.14 \times 20 \, \text{ft}
]
Now, performing the multiplication:
[
\text{Circumference} = 62.8 \, \text{ft}
]
Thus, the circumference of the circle is 62.8 feet.
Explanation
The circumference of a circle is essentially the distance around it, much like the perimeter for polygons. It is directly related to the diameter, which is the longest distance across the circle, passing through the center. The relationship between the diameter and circumference is a fundamental aspect of circles and is defined mathematically using the constant ( \pi ) (pi).
Pi (( \pi )) is a special mathematical constant that represents the ratio of the circumference of any circle to its diameter. This ratio is approximately equal to 3.14, but it is an irrational number, meaning it has an infinite number of non-repeating decimal places.
When calculating the circumference, it is important to use the correct formula, and ensure that all measurements are in the same unit, which in this case is feet. The calculation demonstrates the linear relationship between the diameter and the circumference; doubling the diameter will double the circumference.
Knowing the circumference is useful in various real-life applications, such as determining the length of material needed to cover or encircle a circular object, or calculating distances in circular tracks or pathways. Understanding these concepts is essential not just in mathematics but also in fields like engineering, architecture, and physics, where circular shapes and measurements frequently occur.