The diameter of a circular rug is 34 inches. What is the circumference?
The correct answer and explanation is:
To find the circumference of a circular rug, we use the formula: Circumference=π×diameter\text{Circumference} = \pi \times \text{diameter}
Given:
- Diameter = 34 inches
- Use π≈3.14\pi \approx 3.14
Circumference=3.14×34=106.76 inches\text{Circumference} = 3.14 \times 34 = 106.76 \text{ inches}
Correct Answer: 106.76 inches
Explanation (300 words)
The concept of circumference comes from geometry and refers to the total distance around a circle. Think of it as the circle’s perimeter—the measurement you’d get if you took a string and wrapped it exactly once around the edge of the circular rug, then measured the length of that string.
To calculate the circumference, we rely on the mathematical constant π\pi (pi), which is the ratio of a circle’s circumference to its diameter in all circles. This ratio is approximately 3.14159, but in most practical situations, we use the rounded value 3.14 unless more precision is required.
In this problem, we are given the diameter of the rug, which is 34 inches. The diameter is the distance across the circle, passing through the center. Because the circumference formula is: Circumference=π×diameter\text{Circumference} = \pi \times \text{diameter}
we substitute the given diameter: Circumference=3.14×34=106.76\text{Circumference} = 3.14 \times 34 = 106.76
This tells us that if you walked around the edge of the rug, you’d travel 106.76 inches.
Understanding this is important not just in academic settings, but in practical real-life applications. For example, if you were buying trim or material to border a circular table or rug, you’d need to know the circumference. This formula also appears in physics, engineering, and even art and architecture.
In summary, the circumference is calculated by multiplying the diameter by π\pi. In this case, the circular rug with a diameter of 34 inches has a circumference of 106.76 inches.