Find the radius from the cylinder volume
When the volume of a cylinder is given, you can solve for the missing radius using the cylinder formula:
[
V=\pi r^2 h
]
Here, (V) is volume, (r) is radius, and (h) is height.
Steps
- Write the formula with the given volume and height.
- Isolate (r^2) by dividing both sides by (\pi h):
[
r^2=\frac{V}{\pi h}
]
- Take the square root of both sides:
[
r=\sqrt{\frac{V}{\pi h}}
]
- Simplify the radical or fraction if possible. If the answer is exact, leave it in simplest exact form unless a decimal is requested.
Check your answer
Substitute the radius back into (V=\pi r^2 h). If it gives the original volume, your radius is correct.
Common reminders
- Use the radius, not the diameter.
- Keep units consistent.
- A cylinder’s radius must be positive.
If the problem includes a numerical approximation for (\pi), follow the instructions carefully and simplify the final result as much as possible.