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Figure 1. The cross-sectional area of a cylinder is equal to the area of a circle if cut parallel to the circular base.[1]
The cross-sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point.[2]
For example, the cross-section of a cylinder - when sliced parallel to its base - is a circle. Thus, the cross-sectional area of this slice is the area of a circle with the radius equal to the radius of the provided cylinder.
Uses
The cross-sectional area of some shape is important in many different applications. The cross-section of a series of pipes carrying water helps to determine the speed and pressure with which the water flows through the pipe, especially if there is some change in the cross-sectional area of the pipe at some point. Using Bernoulli's equation, changes in the cross-sectional area of a pipe can be used to determine how other variables such as water pressure and speed must change to accommodate for this pipe change. As a result of this, cross-sectional area of pipes must be taken into account when building hydroelectric dams - particularly the penstocks - for hydroelectric power generation.
Additionally, the cross-sectional area is important when looking at nuclear reactions. The cross-section of some nucleus is used to define the effective size of a nucleus, and thus this value can be used to express the probability of some nuclear reaction taking place.[3] As well, the neutron cross section is particularly important as it expresses how likely a reaction between a neutron and a target nucleus is, the basis for nuclear fission.
For Further Reading
References
A cross section is the shape we get when cutting straight through an object.
|
The cross section of this object is a triangle. |
It is like a view into the inside of something made by cutting through it.
| This is a cross-section of a piece of celery. |
Geometry
In geometry it is the shape made when a solid is cut through by a plane.
Example:
The cross section of this circular cylinder is a circle
We don't draw the rest of the object, just the shape made when you cut through.
Example:
The cross section of a rectangular pyramid is a rectangle
Cross sections are usually parallel to the base like above, but can be in any direction.
The vertical cross section through the center of this torus is two circles!
And the horizontal cross section is an annulus
More Examples of Cross Sections
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