If a circle has a radius of 3 cm, what is its circumference?

To find the circumference of a circle, the formula to use is:

[ C = 2\pi r ]

where ( C ) is the circumference and ( r ) is the radius of the circle.

In this case, the radius of the circle is given as 3 cm. Plugging this value into the formula gives:

[ C = 2\pi(3) ]

This simplifies to:

[ C = 6\pi \text{ cm} ]

This means the circumference of the circle is ( 6\pi ) cm.

The correct answer reflects the appropriate application of the formula for circumference and correctly substitutes the value for the radius. Other options such as ( 9\pi ) cm, ( 12\pi ) cm, and ( 15\pi ) cm would arise from incorrect calculations or misapplications of the circumference formula. For example, multiplying the radius by 3, instead of 2, would lead to the wrong answer. The important takeaway is the proper use of the formula and understanding that the circumference is directly related to the radius through a factor of ( 2\pi ).