Final answer:
To find the circumference of a cone with a known volume and height, use the volume formula to solve for the radius, then substitute that radius into the circumference formula to get the answer. In this case, the circumference of the cone is 8π units.
Step-by-step explanation:
To find the circumference of a cone with a volume of 48π units3 and height of 9 units, we start by using the formula for the volume of a cone, which is V = (1/3)πr2h. We can rearrange this formula to solve for the radius r.
First, we substitute the given values into the formula:
48π = (1/3)πr2(9)
48π = 3πr2
r2 = 16
r = 4 units
Now that we have the radius, we can calculate the circumference, which is given by the formula C = 2πr.
Plugging the radius into the circumference formula:
C = 2π(4)
C = 8π units
Therefore, the circumference of the cone is 8π units.