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The fourteenth problem of the Moscow Mathematical calculates the volume of a frustum. Problem 14 states that a pyramid has been truncated in such a way that the top area is a square of length 2 units, the bottom a square of length 4 units, and the height 6 units, as shown. The volume is found to be 56 cubic units, which is correct. [1]
The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex":
The formula for the volume of a frustum of a paraboloid [23] [24] is: V = (π h/2)(r 1 2 + r 2 2), where h = height of the frustum, r 1 is the radius of the base of the frustum, and r 2 is the radius of the top of the frustum. This allows us to use a paraboloid frustum where that form appears more appropriate than a cone.
A spherical segment Pair of parallel planes intersecting a sphere forming a spherical segment (i.e., a spherical frustum) Terminology for spherical segments.. In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes.
For a regular n-gonal bifrustum with the equatorial polygon sides a, bases sides b and semi-height (half the distance between the planes of bases) h, the lateral surface area A l, total area A and volume V are: [2] and [3] = (+) () + = + = + + Note that the volume V is twice the volume of a frusta.
Volume of Pyramid Volume of Frustum — The 14th problem of the Moscow Mathematical Papyrus calculates the volume of a frustum . Problem 14 states that a pyramid has been truncated in such a way that the top area is a square of length 2 units, the bottom a square of length 4 units, and the height 6 units, as shown.
A frustum is a portion of a solid that lies between two parallel planes cutting this solid. It may also refer to: Frustum (aerospace), a kind of payload fairing; Frustum (computer graphics), the three-dimensional region visible on the screen; Mount Frustum, a landform in Antarctica
A view frustum The appearance of an object in a pyramid of vision When creating a parallel projection, the viewing frustum is shaped like a box as opposed to a pyramid.. In 3D computer graphics, a viewing frustum [1] or view frustum [2] is the region of space in the modeled world that may appear on the screen; it is the field of view of a perspective virtual camera system.