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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":
A hopper is a large, inverted pyramidal or conical container used in industrial processes to hold particulate matter or flowable material of any sort (e.g. dust, gravel, nuts, or seeds) and dispense these from the bottom when needed. In some specialized applications even small metal or plastic assembly components can be loaded and dispensed by ...
Assembled tremie placing concrete underwater Hopper, pipes and lifting cap components of a tremie concrete placement tube. A tremie is a watertight pipe, usually of about 250 mm inside diameter (150 to 300 mm), [1] with a conical hopper at its upper end above the water level. It may have a loose plug or a valve at the bottom end.
If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =.. This may also be written as = (), where φ is half the cone angle, i.e., φ is the angle between the rim of the cap and the direction to the middle of the cap as seen from the sphere center.
In a conical system, as the rotating flow moves towards the narrow end of the cyclone, the rotational radius of the stream is reduced, thus separating smaller and smaller particles. The cyclone geometry, together with volumetric flow rate, defines the cut point of the cyclone. This is the size of particle that will be removed from the stream ...
Stop pouring the material when the pile reaches a predetermined height or the base a predetermined width. Rather than attempt to measure the angle of the resulting cone directly, divide the height by half the width of the base of the cone. The inverse tangent of this ratio is the angle of repose.
The hypervolume of a four-dimensional pyramid and cone is = where V is the volume of the base and h is the height (the distance between the centre of the base and the apex). For a spherical cone with a base volume of =, the hypervolume is
A cushion filled with stuffing. In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.