Find the diameter of a circle with circumference 150.72 inches.
Find the diameter of a circle with circumference 150.72 inches.
The Correct Answer and Explanation is:
Correct Answer:
The formula for the circumference of a circle is: C=πdC = \pi d
Where:
- CC is the circumference
- π\pi (pi) is approximately 3.1416
- dd is the diameter
We are given the circumference C=150.72C = 150.72 inches. To find the diameter dd, rearrange the formula: d=Cπd = \frac{C}{\pi} d=150.723.1416≈48d = \frac{150.72}{3.1416} \approx 48
Answer: The diameter is approximately 48 inches.
Explanation:
To determine the diameter of a circle when the circumference is known, we rely on the fundamental relationship between the circumference and diameter. This relationship is expressed through the equation: C=πdC = \pi d
This means the circumference (the distance around the edge of a circle) is equal to pi times the diameter. Pi, denoted by the Greek letter π\pi, is a mathematical constant approximately equal to 3.1416, and it represents the ratio of the circumference to the diameter for any circle.
When you’re given the circumference and asked to find the diameter, you simply rearrange the formula to isolate dd: d=Cπd = \frac{C}{\pi}
In this specific case, the circumference provided is 150.72 inches. Dividing this value by π\pi (approximately 3.1416), we get: d=150.723.1416≈48d = \frac{150.72}{3.1416} \approx 48
Therefore, the diameter of the circle is approximately 48 inches.
This result makes intuitive sense because the diameter is always a little less than one-third of the circumference, due to the value of pi. Since pi is a little more than 3, dividing the circumference by pi reduces the value to about one-third.
Understanding this relationship helps in various real-life applications, such as determining the size of circular objects like wheels, pipes, or plates. Whether in engineering, carpentry, or crafts, being able to convert between circumference and diameter is a key geometric skill.
