What’s the exact circumference of a circle with diameter 12 inches? question 30 options: inches inches inches inches
The Correct Answer and Explanation is:
To calculate the circumference of a circle, you can use the formula:
[
C = \pi \times d
]
where:
- ( C ) is the circumference,
- ( \pi ) (pi) is approximately 3.14 or 22/7, and
- ( d ) is the diameter of the circle.
In this case, the diameter ( d ) is given as 12 inches. Substituting this value into the formula, we get:
[
C = \pi \times 12 \text{ inches}
]
Using ( \pi \approx 3.14 ):
[
C \approx 3.14 \times 12 = 37.68 \text{ inches}
]
Thus, the exact circumference of the circle with a diameter of 12 inches is approximately 37.68 inches.
Explanation of the Calculation Process
- Understanding the Circle: A circle is a two-dimensional shape where all points are equidistant from the center. The distance from the center to any point on the circle is called the radius, while the longest distance across the circle, passing through the center, is the diameter. The circumference is the total distance around the circle.
- Formula for Circumference: The circumference can be calculated using either the diameter or the radius. The formula using the diameter is straightforward and efficient, especially when the diameter is provided directly, as in this case.
- Substituting the Diameter: Knowing the diameter is 12 inches, we substitute this into the formula ( C = \pi \times d ). This substitution allows us to find the circumference without needing to calculate the radius first, simplifying the process.
- Using Pi: The value of ( \pi ) is a constant, roughly equal to 3.14. In mathematical calculations, it can be expressed as a fraction (22/7) or used as a rounded decimal. The choice of approximation can depend on the level of precision required, but 3.14 is sufficient for many practical calculations.
- Final Calculation: Multiplying 12 inches by the value of ( \pi ) gives the circumference as approximately 37.68 inches. This result can be significant in various real-world applications, such as measuring lengths of circular materials or determining the amount of fencing required for a circular garden.
Therefore, the correct answer to the question is 37.68 inches.