Final answer:
To find the radius of a cone given its volume of 16 cm³ and height of 12 cm, we use the formula for the volume of a cone, rearrange it to solve for the radius, and then calculate its value.
Step-by-step explanation:
This is asking for the radius of a cone given the height and volume of the cone. We can determine the radius by using 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. With the volume of the cone given as 16 cm³ and the height as 12 cm, we would rearrange the formula to solve for r: V = (1/3)πr²h. 16 = (1/3)πr²(12). Firstly, multiply by 3 on both sides: 48 = πr²(12). Then, divide by 12: 4 = πr². Now, divide by π to isolate r²: r² = 4/π. Finally, take the square root to find the radius: r = √(4/π). The calculation will give the radius of the cone in centimeters.