The circumference of a circle varies directly as the radius. A circle with radius 6 in has circumference 37.68 in. Find the circumference of the circle if the radius changes to 12 in. The circumference of the circle with the radius 12 is square in

## Step 1<br />The problem involves the concept of direct variation. In a direct variation, two variables increase or decrease together at the same rate. In this case, the circumference of a circle varies directly with the radius. This means that the ratio of the circumference to the radius is constant.<br /><br />## Step 2<br />We are given that a circle with a radius of 6 inches has a circumference of 37.68 inches. We can use this information to find the constant of variation, \(k\), by dividing the circumference by the radius.<br /><br />### \(k = \frac{C}{r} = \frac{37.68}{6} = 6.28\)<br /><br />## Step 3<br />Now that we have the constant of variation, we can find the circumference of a circle with a radius of 12 inches by multiplying the radius by the constant of variation.<br /><br />### \(C = k \times r = 6.28 \times 12 = 75.36\)