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

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

• A. 5 cm
• B. 10 cm
• C. 15 cm
• D. 20 cm

Answer: (A)

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.

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.