The length of an arc of 0.4 of a circle is 37.68 cm. Find the diameter of the circle.

To solve this problem, we introduce a conditional variable “X”, through which we denote the circumference. Based on the data of the problem, we will compose the following proportion: 0.4 refers to 37.68 centimeters, as 1 refers to X centimeters. Then, based on this proportion, we get the following equation: X = (1 x 37.68) / 0.4. Solving this equation, we get X equal to 94.2 centimeters. Using the formula for the circumference of a circle, we find its diameter equal to 94.2 / 3.14 = 30 centimeters. Answer: the diameter of the circle is 30 centimeters.