Final answer:
To find the circumference of a cone with a volume of 48π cubic units and a height of 9 units, we first calculate the radius using the volume formula, then use the radius to find the circumference, resulting in a circumference of 8π units.
Step-by-step explanation:
The question asks us to find the circumference of a right cone given that the volume is 48π units cubed and the height is 9 units. To solve this, we first use the formula for the volume of a cone, which is V = (1/3)πr²h where V is the volume, r is the radius, and h is the height. Given that V = 48π and h = 9, we can substitute these values into the formula and solve for r.
First, rearrange the formula to solve for the radius squared: r² = 3V/(πh) = 3(48π)/(π(9)) = 16. Then, take the square root of both sides to find the radius: r = √16 = 4 units. Now that we have the radius, we can find the circumference using the formula C = 2πr, which yields C = 2π(4) = 8π units.
Thus, the circumference of the cone in terms of π is 8π units.