A plate has a radius of 5.5 inches. What is the circumference of the plate?
The correct answer and explanation is:
To find the circumference of a circular plate, we use the formula: Circumference=2πr\text{Circumference} = 2\pi r
where rr is the radius of the circle and π≈3.1416\pi \approx 3.1416.
Given:
- Radius r=5.5r = 5.5 inches
Circumference=2×π×5.5=2×3.1416×5.5\text{Circumference} = 2 \times \pi \times 5.5 = 2 \times 3.1416 \times 5.5 Circumference≈34.5576 inches\text{Circumference} \approx 34.5576 \text{ inches}
Answer: The circumference of the plate is approximately 34.56 inches.
300-Word Explanation:
The concept of circumference refers to the total distance around a circular object. In the context of a plate, this is the measurement of the outer edge of the circular dish. When you walk around the edge of a circle, the distance you travel is called the circumference.
To calculate this, we use the mathematical constant π (pi), which represents the ratio of the circumference of a circle to its diameter. The value of π\pi is approximately 3.1416, although it continues infinitely without repeating.
In this case, the radius of the plate is given as 5.5 inches. The radius is the distance from the center of the circle to any point on its boundary. The diameter is simply twice the radius, so 2×5.5=112 \times 5.5 = 11 inches.
Plugging the radius into the circumference formula: Circumference=2πr=2×3.1416×5.5=34.5576 inches\text{Circumference} = 2\pi r = 2 \times 3.1416 \times 5.5 = 34.5576 \text{ inches}
This calculation means that if you took a string and wrapped it exactly once around the edge of the plate, then laid it out flat and measured it, it would be about 34.56 inches long.
Understanding circumference is important in many real-world applications, from designing plates and wheels to building circular fences. It helps in estimating lengths, understanding proportions, and solving geometric problems. By applying a simple formula involving pi and the radius, we gain a practical and precise way to measure the boundary of any circular object.