What is the height of a cone with a base diameter of 16 inches proportional to a cone with a base diameter of 22 inches and a height of 4 feet?

To find the height of the smaller cone with a base diameter of 16 inches, we can use the principle of proportionality between similar cones. The ratio of the diameters (16 inches to 22 inches) is 16/22, which simplifies to 8/11. Since the height of the larger cone is 4 feet (or 48 inches), the height of the smaller cone can be calculated as follows: ( \text{Height} = \frac{8}{11} \times 48 \approx 34.91 ) inches. Thus, the height of the smaller cone is approximately 34.91 inches.