Final answer:
To find the height of the cylinder with a given volume of 144π cubic inches and a radius of 4 inches, we use the formula V = πr²h and solve for h, resulting in a height of 9 inches.
Step-by-step explanation:
The question asks about determining the height of a cylinder when given the volume and the radius. To find the height (h) of the cylinder, we use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height. The volume of the cylinder is given as 144π cubic inches and the radius is given as 4 inches.
First, substitute the known values into the formula:
- V = π × (4 inches)² × h
- 144π = π × 16 × h
Next, solve for h:
- h = 144π / (16π)
- h = 144 / 16
- h = 9 inches
Therefore, the height of the cylinder is 9 inches.