Calculate cylinder volume from circumference and length, sphere dimensions from a known circumference, radius, diameter or volume, and spherical cap or common solid volumes in metric or US units.
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Volume From Circumference Formula
The following formula calculates a circular cylinderโs volume from its base circumference and axial length. Circumference alone does not determine a general solidโs volume. Choose Cylinder from circumference for this articleโs table and examples. Choose a sphere mode when the circumference is a great circle; its volume is V = Cยณ/(6ฯยฒ).
- Where V is the cylinder volume (inยณ)
- C is the circular base circumference (in)
- L is the axial cylinder length (in)
For a circular cylinder, divide the base circumference by 2ฯ to obtain the radius, then multiply ฯ times the squared radius by the axial length. The calculator also retains sphere, spherical cap, hemisphere and common-solid modes, each with its own dimensions.
| Circumference (in) | Length (in) | Volume (inยณ) |
|---|---|---|
| 6 | 6 | 17.189 |
| 6 | 12 | 34.377 |
| 6 | 24 | 68.755 |
| 6 | 36 | 103.132 |
| 8 | 6 | 30.558 |
| 8 | 12 | 61.115 |
| 8 | 24 | 122.231 |
| 8 | 36 | 183.346 |
| 10 | 6 | 47.746 |
| 10 | 12 | 95.493 |
| 10 | 24 | 190.986 |
| 10 | 36 | 286.479 |
| 12 | 6 | 68.755 |
| 12 | 12 | 137.510 |
| 12 | 24 | 275.020 |
| 12 | 36 | 412.530 |
| 16 | 6 | 122.231 |
| 16 | 12 | 244.462 |
| 16 | 24 | 488.924 |
| 16 | 36 | 733.386 |
| Assumes a circular cylinder. Formula: V = Cยฒ ร L / (4ฯ). Units shown: inches (in) and cubic inches (inยณ). | ||
How to Calculate Volume From Circumference?
The following example problems outline how to calculate Volume From Circumference.
Example Problem #1:
- First, determine the total circumference (in).
- The total circumference (in) is given as 20.
- Next, determine the length (in).
- The length (in) is provided as 5.
- Finally, calculate the Volume From Circumference using the equation above:
V = Cยฒ * L / (4ฯ)
The values given above are inserted into the equation below:
V = pi * (20/(2*pi))^2 * 5 = 159.155 (inยณ)
Example Problem #2:
The variables needed for this problem are provided below:
total circumference (in) = 60
length (in) = 3
Entering these values and solving gives:
V = Cยฒ * L / (4ฯ) = 859.437 (inยณ)
