What is the formula for the circumference of a circle?

The formula for the circumference of a circle is directly related to its radius and diameter. The circumference can be calculated in two equivalent ways: using the radius and using the diameter.

When using the radius, the formula is (2 \times \pi \times \text{radius}). Here, the radius is multiplied by 2 and then by (\pi) to give the total distance around the circle.

When using the diameter, the formula is (\pi \times \text{diameter}). The diameter is twice the length of the radius, and thus both formulas yield the same result. Since the diameter is essentially (2 \times \text{radius}), substituting that into the circumference formula confirms that ( \pi \times \text{diameter} = 2 \times \pi \times \text{radius}).

Therefore, stating that both formulas give the circumference of a circle is accurate and makes the selected answer correct. The relationship between the different ways of calculating the circumference underscores an important concept in geometry regarding circular measurements.