Circumference
Calculating the circumference of a circle helps in many ways. Suppose you were building a circular pool with a diameter of 30 feet, and you want to put a decorative border around the outside edge. You'd need to know the length of the border material required to go around the entire pool. To find this, you would need to calculate the circumference of the circle. Fortunately, calculating circumference is easy, and we can do it in just a few steps.
Why you need pi to calculate circumference
First, you need pi. No, we're not talking about dessert -- we're talking about the ratio of a circle's circumference to its diameter. Fortunately, we don't need to actually calculate pi, since ancient cultures such as the Egyptians and Greeks already accomplished this thousands of years ago. The value of pi is approximately 3.14259 -- although the number contains an infinite number of non-repeating digits!
The formula is simple: C = 2πr
Where "C" represents the circumference, π represents pi, and "r" represents the radius.
You could also write the formula like this: C = πd
Where "d" represents the diameter of a circle.
Example 1:A bicycle tire has a diameter of 26 inches. What is the circumference of the tire?
To solve this problem, we can use the formula for the circumference of a circle, which is C = πd, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and d is the diameter of the circle.
We are given that the diameter of the bicycle tire is 26 inches, so we can substitute this value into the formula:
C = πd, C = 3.14 * 26, C = 81.7 inches
Therefore, the circumference of the bicycle tire is approximately 81.7 inches.
Example 2:A circular swimming pool has a diameter of 30 feet. The pool has a walkway around it that is 5 feet wide. What is the total area of the walkway? What is the total circumference of the pool and the walkway?
To solve this problem, we can start by finding "r" the radius of the pool, which is half of the diameter:
r = d/2 = 30/2 = 15 feet
Next, we can find the radius of the pool and the walkway together "R", by adding the 5 feet of the walkway to the radius of the pool:
R = r + 5 = 15 + 5 = 20 feet
Finally, we can find the total circumference of the pool and the walkway together by adding the circumference of the larger circle with radius R to the circumference of the pool with radius r:
Circumference of larger circle: 2πR = 2 * 3.14 * 20 ≈ 125.7 feet
Circumference of pool: 2πr = 2 * 3.14 * 15 ≈ 94.2 feet
Total circumference of pool and walkway is equal to the Circumference of the larger circle plus the Circumference of the pool which is approximately: 125.7 + 94.2 ≈ 219.9 feet
Topics related to the Circumference
Flashcards covering the Circumference
Common Core: 7th Grade Math Flashcards
Practice tests covering the Circumference
MAP 7th Grade Math Practice Tests
Common Core: 7th Grade Math Diagnostic Tests
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