The diameter of a circle is 2 inches. What is the circle’s circumference?
The Correct Answer and Explanation is:
Correct Answer:
The circumference of a circle with a diameter of 2 inches is π × diameter = π × 2 = 2π inches, which is approximately 6.28 inches.
Explanation:
The circumference of a circle refers to the distance around the edge of the circle — essentially, its perimeter. To calculate the circumference, we use a well-known formula from geometry: Circumference=π×Diameter\text{Circumference} = \pi \times \text{Diameter}
Here, π (pi) is a mathematical constant that represents the ratio of a circle’s circumference to its diameter. It is an irrational number, meaning it has no exact decimal representation, but it is commonly approximated as 3.14 or more precisely 3.14159.
In this problem, we are told that the diameter of the circle is 2 inches. The diameter is the distance across the circle through its center. Plugging this value into the formula: Circumference=π×2=2π inches\text{Circumference} = \pi \times 2 = 2\pi \text{ inches}
This is the exact answer. However, if a numerical approximation is needed, we can multiply π by 2: 2×3.14159≈6.28318 inches2 \times 3.14159 \approx 6.28318 \text{ inches}
Rounded to two decimal places, the circumference is approximately 6.28 inches.
Understanding the relationship between a circle’s diameter and its circumference is fundamental in both math and real-life applications. For example, if you roll a circular object (like a wheel or a coin) one full turn along a surface, the distance it travels is equal to its circumference. So, a coin with a 2-inch diameter will roll about 6.28 inches in one full revolution.
This concept is also the basis for converting between rotational motion and linear motion in mechanics, making it essential in fields like engineering, physics, and design.
