在铁路运输中估计剩余的冷煤的数量,使用旋转的LiDAR

The volume of a fuel tank mounted on the wing of a jet aircraft can be modeled using the concept of solids of revolution. In this case, the tank is formed by rotating a two-dimensional region, defined by a mathematical function, about the x-axis. The region extends along the axis from zero to two meters, and the resulting three-dimensional shape is symmetric about the axis of rotation. Because the boundary curve lies directly against the axis, the disk method is an appropriate technique for...

Air content measurement in concrete is critical for ensuring structural integrity and durability of concrete structures, especially in environments prone to severe weather conditions. Accurate air content analysis optimizes concrete's resistance to freeze-thaw cycles and enhances its workability and strength. Several methods are standardized under ASTM guidelines to measure the air content in fresh concrete, each suitable for different concrete types and conditions.
The pressure method,...

For solids whose cross-sectional areas vary in a predictable way, volume can be determined by integrating these areas along an axis perpendicular to the slices. This approach is particularly useful for polyhedral solids, where classical geometric formulas may not be immediately applicable. A tetrahedron provides a clear example of how cross-sectional integration can be applied to a three-dimensional object with continuously changing geometry.Consider a tetrahedron with height h and a base that...

Volatilization gravimetry is an analytical technique that measures the mass lost due to the volatilization of the substance. This technique is used to estimate the amount of volatile material in a sample. To perform this method, heat a known amount of the sample to a high temperature in a crucible or other suitable vessel. The volatile substance in the sample evaporates, and the vapor is completely expelled from the crucible either by heating the sample or bubbling a stream of inert gas through...

Volume calculation often begins with simple geometric solids. For example, the volume of a rectangular box is obtained by multiplying the area of its base by its height. This straightforward approach relies on the fact that the cross-sectional area of the box remains constant throughout its length. Many real-world objects, however, do not have uniform cross-sections, and their volumes cannot be determined using elementary geometric formulas.To address this limitation, the Slicing Method...