A circle has a circumference of 3.14 units.
What is the diameter of the circle?
Use 3.14 for π and enter your answer as a decimal.
The Correct Answer and Explanation is :
To find the diameter of a circle when given its circumference, we can use the formula that relates the circumference (C) to the diameter (d):
[
C = \pi \times d
]
Here, (\pi) is a mathematical constant approximately equal to 3.14. Given the circumference of the circle is 3.14 units, we can set up the equation as follows:
[
3.14 = 3.14 \times d
]
To solve for the diameter (d), we can rearrange the formula:
[
d = \frac{C}{\pi}
]
Substituting the known values:
[
d = \frac{3.14}{3.14} = 1
]
Thus, the diameter of the circle is 1.0 units.
Explanation:
- Understanding the Relationship: The relationship between the circumference and diameter is fundamental in circle geometry. The circumference is the distance around the circle, while the diameter is the longest straight line that can be drawn through the circle, connecting two points on its boundary.
- Using Pi ((\pi)): The constant (\pi) is essential in circle calculations. It is defined as the ratio of the circumference of any circle to its diameter. This means that no matter the size of the circle, if you divide the circumference by the diameter, you will always get approximately 3.14 (or more accurately, 3.14159).
- Real-World Applications: Understanding the relationship between diameter and circumference is not just an academic exercise; it has practical applications in various fields, including engineering, architecture, and manufacturing. For instance, when designing circular components or wheels, knowing the diameter can help in ensuring the part fits correctly within a system.
- Conclusion: In conclusion, when given the circumference of a circle, calculating the diameter is straightforward using the formula (d = \frac{C}{\pi}). With a circumference of 3.14 units, we determined the diameter to be 1.0 units. This relationship is foundational in mathematics and is crucial for practical applications in everyday life.