Whats the circumference of a circle with a diameter of 12 ft?
The Correct Answer and Explanation is :
The circumference (C) of a circle is calculated using the formula:
[
C = \pi \times d
]
where (d) is the diameter of the circle, and (\pi) (pi) is approximately 3.14159.
Step 1: Identify the diameter
In this case, the diameter (d) is given as 12 feet.
Step 2: Apply the formula
Substitute the diameter into the circumference formula:
[
C = \pi \times 12
]
Using the approximation of (\pi \approx 3.14159):
[
C = 3.14159 \times 12
]
Step 3: Perform the multiplication
[
C \approx 37.6991 \text{ feet}
]
So, the circumference of the circle is approximately 37.7 feet.
Explanation
The circumference of a circle is essentially the distance around the edge of the circle, also known as the perimeter. The relationship between the circumference and the diameter of the circle is directly proportional—this means that the circumference will always be (\pi) times the diameter. Since the value of (\pi) is irrational (it cannot be expressed exactly as a simple fraction), we often use approximations like 3.14159 or 22/7 for practical calculations.
In this case, the diameter of the circle is 12 feet, so the circumference is simply (3.14159 \times 12), which gives us the result of approximately 37.7 feet. This concept is important in many practical fields, such as construction, engineering, and even in areas like art and design, where understanding the size of circular objects or spaces is essential.
The circumference formula shows that for any circle, if you know the diameter, you can easily calculate the total distance around the circle, which helps in various applications, such as measuring or creating circular objects and pathways.