Final answer:
The length of the radius of the base of the cone is 2 inches.
Step-by-step explanation:
To find the length of the radius of the base of the cone, we can rearrange the formula for the volume of a cone: V = 1/3πr²h. Given that the volume of the cone is 16π³ and the height is 12 inches, we can substitute those values into the formula:
16π³ = 1/3πr²(12)
Simplifying the equation:
16 = r²(4)
Dividing both sides by 4:
4 = r²
Taking the square root of both sides:
r = 2
Therefore, the length of the radius of the base of the cone is 2 inches.