Final answer:
The diameter of the cone is 4√3 cm, which is approximately 6.93 cm when rounded to two decimal places.
Step-by-step explanation:
To find the diameter of the cone, we first need to identify the formula for the volume of a cone, which is V = (1/3)πr^2h. Given that the volume (V) of the ice cream cone is 12π cubic cm and the height (h) is 9 cm, we can set up the equation to solve for the radius (r):
12π = (1/3)πr^2(9)
We can simplify this equation by dividing both sides by π and multiplying both sides by 3/9 (which is the reciprocal of 1/3 times 9):
12 = r^2
Therefore, r = √12 cm. To find the diameter, which is twice the radius, we calculate:
Diameter = 2r = 2(√12) cm = 2(√4√3) cm = 4√3 cm
The diameter of the cone is 4√3 cm or approximately 6.93 cm when rounded to two decimal places.