What is the exact circumference of a circle with a diameter of 19 inches?
The Correct Answer and Explanation is :
The circumference of a circle can be calculated using the formula:
[
C = \pi \times d
]
where ( C ) is the circumference and ( d ) is the diameter of the circle. Given that the diameter of the circle is 19 inches, we can substitute this value into the formula:
[
C = \pi \times 19
]
Since ( \pi ) (pi) is approximately 3.14159, we can calculate the circumference as follows:
[
C = 3.14159 \times 19
]
[
C \approx 59.6903 \text{ inches}
]
Therefore, the exact circumference of the circle is approximately 59.69 inches.
Explanation:
A circle is a shape where all points on the boundary are equidistant from the center, and the diameter is the distance across the circle, passing through its center. The key relationship between the diameter and the circumference is established by the constant ( \pi ), which is the ratio of the circumference of any circle to its diameter. This ratio remains constant regardless of the size of the circle.
The value of ( \pi ) is a transcendental number, meaning it cannot be exactly represented as a simple fraction, though it is commonly approximated as 3.14159. In mathematics, this constant is vital in many formulas relating to circles and spheres. It is used in calculating not only the circumference but also the area of a circle, the volume of a sphere, and many other geometric properties.
In practical terms, the formula ( C = \pi \times d ) allows us to find the circumference if we know the diameter. In this case, with a diameter of 19 inches, multiplying this value by ( \pi ) gives a circumference of approximately 59.69 inches, rounding to two decimal places.
This formula is essential in many fields, from engineering to architecture, where circular shapes are commonly encountered.