If the circumference of a circle is 31.4 cm, what is its radius?

To find the radius of a circle given its circumference, you can use the relationship between circumference (C) and radius (r) described by the formula:

[ C = 2\pi r ]

In this case, the circumference is given as 31.4 cm. To solve for the radius, you would rearrange the formula to isolate r:

[ r = \frac{C}{2\pi} ]

Substituting the given circumference into the formula:

[ r = \frac{31.4}{2\pi} ]

Using the approximation ( \pi \approx 3.14 ):

[ r = \frac{31.4}{2 \times 3.14} ]

[ r = \frac{31.4}{6.28} ]

[ r = 5 \text{ cm} ]

Thus, the calculation confirms that the radius of the circle is indeed 5 cm. This directly shows how the formula relates the circumference to the radius, and using the specific value for the circumference leads us to the radius accurately.