Oblique Cylinder Volume Calculator
Oblique cylinder volume uses the formula V = pi r squared h, where h is perpendicular height. For a tilted cylinder with radius 4 cm, slant length 12 cm, and 60 degree tilt, height is 10.39 cm, giving a volume of 522.36 cm3. Calculate volume from perpendicular height or slant angle below.
Calculator
Volume of an Oblique Cylinder
An oblique cylinder (also known as an inclined cylinder or slanted cylinder) is a cylinder where the sides are not perpendicular to the bases. The oblique cylinder leans to one side, unlike a standard right cylinder that stands straight.
The cylinder volume formula for an oblique cylinder is the same as for a right cylinder: V = π × r² × h. The key difference is that the height (h) must be the perpendicular height: the shortest distance between the two parallel bases: not the length of the slanted side.
This works because of Cavalieri's principle: two 3D solids with equal cross-sectional areas at every height have the same volume. Tilting a cylinder does not change the area of circular cross-sections at any height.
Slide to tilt the cylinder and see how perpendicular height stays constant
Working from slant length and angle
The volume of a slanted cylinder uses the slant angle and the side length instead of the perpendicular height. This approach is practical when the perpendicular height is difficult to measure directly.
The slanted cylinder volume formula is:
Where r is the radius of the cylinder, L is the side length (slant length), and θ is the slant angle between the side and the base.
To calculate the volume of a slanted cylinder, follow these 6 steps:
- Find the radius, side length, and slant angle of the cylinder.
- Square the radius.
- Multiply the result by Pi (π).
- Take the sin of the angle.
- Multiply the sin by the side length.
- Multiply the results from steps 3 and 5 together. The result is the slanted cylinder volume.
Slanted walls and Cavalieri principle
This tool calculates volume for tilted cylinders. By Cavalieri's Principle, a tilted cylinder holds the same volume as a straight cylinder of the same vertical height.
Perpendicular height from slant angle
The formula is V = pi r squared h, where h is vertical height. If you know slant length and tilt angle, height is slant length times the sine of the angle.
Frequently Asked Questions
What defines an oblique cylinder?
An oblique cylinder is a cylinder whose central axis is not perpendicular to its flat bases. In simpler terms: the top and bottom circles are parallel, but the sides lean over at an angle rather than standing straight up.
How do you calculate the perpendicular height?
If you know the leaning angle and the slanted length of the side (slant height), you use trigonometry. The formula is: Perpendicular Height = Slant Height × sin(angle).
Is the volume of an oblique cylinder smaller than a right cylinder?
No. Assuming they both share the exact same radius and the exact same perpendicular height, an oblique cylinder holds the same volume as a straight right cylinder.
Why can't I just use the slanted side length as height?
Because volume relies on true 3D space, taking the slanted length artificially inflates the height variable. Think of a leaning ladder: the ladder itself is 10 feet long (slant height), but it only reaches 8 feet up the wall (perpendicular height).
What is the formula applied by this calculator?
The calculator first finds perpendicular height using h = slant × sin(angle), then automatically executes the standard V = πr²h formula, outputting your answer instantly.