The rim of the basket has a radius of 9 inches. What is the approximate circumference of the basket? Use pi equals 3.14. Explain why 3.14 is used when finding the circumference of a circles.
*** Explain why 3.14 is used when finding the circumference of circles.
thousands of years ago it was learned that the ratio of the circumference to the diameter of a circle is pi = 3.14159265...
This is true for all circles:
c = pi * d
or,
c = 2pi * r
To find the circumference of a circle, we use the formula:
Circumference = 2 * π * radius
Given that the radius of the basket is 9 inches, we can substitute this value into the formula:
Circumference = 2 * 3.14 * 9
Simplifying the expression:
Circumference = 18 * 3.14
Multiplying the values:
Circumference ≈ 56.52 inches
Now, let's discuss why we use 3.14 (approximately) when finding the circumference of a circle. The number π (pi) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction or a finite decimal.
The approximate value of π is 3.14, which is widely used in calculations involving circles because it provides a simple and close approximation of the true value. In reality, π is a transcendental number with an infinite number of decimal places (3.141592653589793...). But using the value 3.14 is usually sufficient for most applications and simplifies calculations.
To find the circumference of a circle, you can use the formula C = 2πr, where C represents the circumference and r represents the radius of the circle. In this case, the given radius is 9 inches.
To calculate the circumference using the formula, you need to substitute the value of π. The value of π, also known as pi, is an irrational number and is approximately equal to 3.14. It is commonly used as an approximation for π because it is easy to work with and gives reasonably accurate results in many calculations involving circles.
Pi (π) is an important mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a fraction or a repeating decimal. Its decimal representation goes on infinitely without a pattern.
Pi is used when finding the circumference of a circle because it relates the diameter or radius of the circle to its circumference. Since the circumference represents the distance around the circle, π helps us calculate this distance accurately. In practical applications, the value of π is often approximated to a decimal like 3.14 or 22/7 for convenience and simplicity in calculations.
In this case, to find the approximate circumference of the basket, you would substitute the value of the radius (9 inches) and the approximation of π (3.14) into the formula C = 2πr:
C = 2 * 3.14 * 9
C ≈ 56.52 inches
Therefore, the approximate circumference of the basket is 56.52 inches.