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Calculate the volume of any prism using the universal formula: V = Base Area × Height. Select your base shape below.
This formula works for any prism, regardless of the base shape. The volume is simply the area of the base multiplied by the height (distance between the parallel bases).
A prism is a 3D shape with two parallel, identical bases connected by rectangular sides. The volume formula V = A × h is universal because you're essentially stacking infinite copies of the base shape to the given height.
Imagine a prism as a stack of thin slices, each with the same shape as the base. The total volume equals one slice's area times the number of slices (height). This principle is called Cavalieri's principle.
Yes! A cylinder is essentially a prism with a circular base. V = πr²h follows the same principle: base area × height.
For oblique prisms, use the perpendicular height (straight distance between bases), not the slant height. The volume formula still applies.
A pyramid tapers to a point, so its volume is V = (1/3) × Base Area × Height—one-third of a prism with the same base and height.
Find the base area using any method (divide into simpler shapes, use coordinates, etc.), then multiply by height. The formula still works!
If two solids have equal cross-sectional areas at every height, they have equal volumes. This explains why oblique and right prisms with the same base and perpendicular height have equal volumes.
Yes, any flat shape can be the base of a prism—triangles, quadrilaterals, regular or irregular polygons, even shapes with curved edges (like a cylinder).