What is the diameter of a circle that has an approximate circumference of 56.52 feet?
The correct answer and explanation is:
To find the diameter of a circle when you know its circumference, you use the formula for the circumference of a circle: C=π×dC = \pi \times d
where:
- CC is the circumference,
- dd is the diameter,
- π\pi (pi) is approximately 3.1416.
Given: C=56.52 feetC = 56.52 \text{ feet}
We need to solve for dd. Rearranging the formula: d=Cπd = \frac{C}{\pi}
Substitute the known values: d=56.523.1416≈18.0 feetd = \frac{56.52}{3.1416} \approx 18.0 \text{ feet}
Therefore, the diameter of the circle is approximately 18 feet.
Explanation (300 words):
The diameter of a circle is the straight line passing from one point on the circle, through its center, to another point on the circle. The circumference is the total distance around the circle.
The relationship between the circumference and diameter is a fundamental property of circles described by the formula: C=πdC = \pi d
Here, π\pi (pi) is a mathematical constant that represents the ratio of a circle’s circumference to its diameter. Pi is approximately 3.1416 but is an irrational number with an infinite number of decimal places.
Given the circumference of 56.52 feet, we want to find the diameter. Since circumference and diameter are directly proportional by π\pi, dividing the circumference by π\pi gives the diameter.
This calculation is straightforward but important in many practical contexts — such as engineering, construction, and design — where you may only measure the circumference (for example, measuring around a pipe or circular object) but need to know its diameter to fit it properly or understand its size.
An approximate value of 18 feet means that if you drew a straight line through the center of this circle from one edge to the opposite edge, that line would measure about 18 feet.
In summary, the diameter is always smaller than the circumference by a factor of π\pi, and knowing one allows you to find the other easily using this fundamental formula. This direct relationship is a cornerstone in geometry and helps in calculations involving circular shapes in real-world applications.