What is the formula for the circumference of a circle in relation to the diameter?

What is the formula for the circumference of a circle in relation to the diameter?

• A. Diagonal = π × radius
• B. Circumference = π × diameter
• C. Circumference = 2 × radius
• D. Circumference = diameter × radius

Answer: (B)

The formula for the circumference of a circle is derived from the relationship between the diameter and the constant π (pi). The circumference refers to the total distance around the circle. The correct formula states that the circumference is equal to π multiplied by the diameter. In mathematical terms, this can be represented as: Circumference = π × diameter. This formula illustrates that for every unit of diameter, the circumference is slightly more than three times that length (since π is approximately 3.14). This relationship is fundamental in both geometry and real-life applications when measuring circular objects. The other options do not accurately represent the correct relationship. For example, while the choice that involves the radius does have a correct formulation—circumference can also be expressed as 2×π×radius—the specific relation to the diameter is represented correctly only in the choice for circumference = π × diameter. Thus, recognizing this formula is crucial for understanding how to work with circles effectively.

The formula for the circumference of a circle is derived from the relationship between the diameter and the constant π (pi). The circumference refers to the total distance around the circle. The correct formula states that the circumference is equal to π multiplied by the diameter.

In mathematical terms, this can be represented as:

Circumference = π × diameter.

This formula illustrates that for every unit of diameter, the circumference is slightly more than three times that length (since π is approximately 3.14). This relationship is fundamental in both geometry and real-life applications when measuring circular objects.

The other options do not accurately represent the correct relationship. For example, while the choice that involves the radius does have a correct formulation—circumference can also be expressed as 2×π×radius—the specific relation to the diameter is represented correctly only in the choice for circumference = π × diameter. Thus, recognizing this formula is crucial for understanding how to work with circles effectively.