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Calculate the volume of an oblique (tilted) prism. The key is using the perpendicular height, not the slant height.
The straight-up distance between bases
Used to calculate the tilt angle
For volume, always use the perpendicular height (straight vertical distance between bases), not the slant height. The formula V = A × h works for both right and oblique prisms!
An oblique prism has the same volume as a right prism with the same base and perpendicular height. This is because every horizontal cross-section has the same area, just shifted sideways.
Imagine slicing the prism into thin horizontal layers. Each layer has the same area whether the prism is tilted or not. The total volume is the sum of all layers, which depends only on base area and perpendicular height.
If two solids have equal cross-sectional areas at every height, they have equal volumes. Named after Italian mathematician Bonaventura Cavalieri (1598-1647).
No! Oblique prisms typically have more surface area because the lateral faces are parallelograms with longer sides than rectangles with the same height.
If you know the slant height and the horizontal offset, use: h = √(slant² - offset²). Or if you know the tilt angle θ from vertical: h = slant × cos(θ).
The Leaning Tower of Pisa (approximately), some modern architectural buildings, parallelogram-shaped packaging, and deck of cards when pushed to one side.
Yes! An oblique cylinder has the same volume as a right cylinder with the same base and perpendicular height: V = πr²h (using perpendicular height).