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How to Calculate Cross-sectional Area

How to Calculate Cross-sectional Area

If you are curious about what exactly is cross sectional area of three-dimensional objects, this article will be an informative read. Here, you will also find a list of formulas for cross sections of various geometrical objects.
ScienceStruck Staff
Geometry is the study of shapes, surfaces, and characteristics of space itself. A large part of high school level geometry focuses on the study of various three-dimensional objects and their properties.
Area is the numerical measurement of the surface expanse of a planar surface. It is generally measured in square meters, square centimeters, or square feet.
Definition
A cross section of any object is an intersection of a plane with that three-dimensional object, with the plane being perpendicular to the longest axis of symmetry passing through it. The area of this plane of intersection is known as the cross-sectional area of the object.
If you have ever sliced a vegetable in two, you already know what a cross section is. The plane of the knife cutting through the vegetable, like a carrot, creates a cross-sectional slice of the object. The area of one such thin slice, made perpendicular to the axis of symmetry of the vegetable, is known as the cross-sectional area.
How is it Calculated?
To know the cross-sectional area of any three-dimensional object, one must first understand what its shape is. To know the shape, you need to first find out the axis of symmetry of the object. Then draw a diagram of the object, along with the axis of symmetry. Draw a plane, which is perpendicular to the axis of symmetry and see what the shape of the intersection is. This is known as taking an orthographic projection of the object, in technical terms.
Draw the shape of the intersection plane in a separate diagram. Depending on the shape of the cross section, the formula for its area calculation will be different. If it is a square, circle, or a triangle, the calculation is simple, but if it's a complex shape, you may have to break it down into simpler ones, for the purpose of calculation. Knowing the dimensions of the object, you can easily calculate the cross section.
Formulas
Three-dimensional Object Formula
Cylinder ∏r2
Pipe (Square) Length2
Sphere ∏r2
Triangular Prism 1/2 x Base x Height
Cone ∏r2
Pipe (Circular) ∏r2

The concept of cross-sectional profile or area of any object finds application in engineering. Just list out some of the above formulas on a chart and stick it in front of your work desk. As and when you find time, just go through the formulas, and within no time you will have memorized all of them.