Final answer:
The height of a cylinder with a volume of 8550 cubic units and a radius of 14 units is found to be approximately 13.85 units after rearranging the volume formula and substituting the known values.
Step-by-step explanation:
The volume of a cylinder is calculated using the formula V = πr²h where V represents the volume, r is the radius and h is the height of the cylinder. To find the height of the cylinder when the volume is 8550 cubic units and the radius is 14 units, we must rearrange the formula to solve for h, which gives us h = V / (πr²).
Using the given values, the calculation for h is as follows:
- Radius (r) = 14 units
- Volume (V) = 8550 cubic units
- h = 8550 / (π × 14²)
Now we plug the values into the equation and solve for h:
- h = 8550 / (3.1416 × 14²)
- h = 8550 / (3.1416 × 196)
- h = 8550 / (616.8569)
- h ≈ 13.85 units
Therefore, the height of the cylinder is approximately 13.85 units.