# 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.

Omkar Phatak

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.

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.

Formulas

Three-dimensional Object |
Formula |

Cylinder | ∏r^{2} |

Pipe (Square) | Length^{2} |

Sphere | ∏r^{2} |

Triangular Prism | 1/2 x Base x Height |

Cone | ∏r^{2} |

Pipe (Circular) | ∏r^{2} |

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.