Final answer:
To calculate the diameter of the cone, the volume formula V = (1/3)πr²h is used with the provided volume and height. After simplifying, the radius is found to be 4 inches, and the diameter is thus twice the radius, which is 8 inches.
Step-by-step explanation:
To find the diameter of a cone with a given volume and height, we can use the formula for the volume of a cone, which is V = (1/3)πr²h. In this case, we are given the volume V = 48π inches cubed and the height h = 9 inches. We are solving for the radius r first, which we can then double to get the diameter.
Plugging in the given values, we have 48π = (1/3)πr²(9). Solving for r², we find r² = (48π / (1/3)π(9)) = 16. Taking the square root of both sides, r = 4 inches. Therefore, the diameter of the circular base, which is twice the radius, is 4 inches × 2 = 8 inches.