What does frustum mean?
A frustum is the solid figure that remains when a cone or pyramid is sliced by a plane parallel to its base and the upper portion is removed. The result is a shape with two parallel faces — a larger base and a smaller 'top' — joined by sloping sides, familiar in everyday objects such as lampshades, buckets, drinking cups, and tapered columns. In mathematics, the frustum has well-established formulas for its volume and surface area, making it a standard topic in geometry courses. The term also appears in engineering, architecture, and computer graphics, where three-dimensional rendering pipelines describe a viewing volume shaped like a frustum. Derived from the Latin frustum, meaning a piece broken off something such as bread, the word entered English in the seventeenth century. Though technical in register, it neatly names a shape so ordinary that few people realize it has a dedicated term.
nounThe portion of a solid figure, typically a cone or pyramid, that lies between one or two parallel planes cutting it — most commonly the part remaining after the top has been sliced off by a plane parallel to the base.
- In geometry: the part of a cone or pyramid lying between its base and a plane parallel to the base that cuts through it.
- More generally: any portion of a solid removed by, or contained between, parallel cutting planes.
"The lampshade is shaped like a frustum, wider at the bottom than at the top."
"To find the volume of a frustum, you need the radii of both circular faces and the perpendicular distance between them."
"Ancient Egyptian architects may have calculated the stone needed for a truncated obelisk by treating its tip as a frustum."
Both plurals are accepted; the Latinate 'frusta' is especially common in formal mathematical texts, while 'frustums' predominates in general usage.
"The sculptor carved several granite frusta for the fountain's stepped base."
A frustum is just a cone or pyramid that got a haircut — and the word itself comes straight from the Latin for a broken-off piece of bread.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of frustum
Frustum derives directly from Latin frustum, meaning a piece broken or cut off something — a morsel of bread, a fragment of food. The Latin noun was adopted into English as a geometrical term in the early modern period, commonly cited as the early seventeenth century, to name precisely this kind of 'cut-off piece' of a solid. Because the word was taken over wholesale rather than evolved through intermediate forms, it retains an unusually direct link to its classical source; its plural 'frusta' likewise preserves the Latin form alongside the anglicized 'frustums'.
How frustum is actually used
A technical term used almost exclusively in mathematics, engineering, computer graphics, and related fields; rarely encountered in everyday conversation. The plural is correctly given as either 'frustums' or the Latinate 'frusta', with 'frusta' common in mathematical writing.
Easily confused with frustum
A pyramid tapers to a single apex point, whereas a frustum is a pyramid or cone whose top has been cut off by a plane parallel to the base.
A cone comes to a point at its apex, while a frustum of a cone is what remains when that pointed top is removed by a slice parallel to the base.