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Cross-Section of a Solid

Another important concept that falls under the category of Solid Geometry is called the cross-section.

cross-section is a shape made by cutting through a solid with a plane.

The cross-section of a cylinder cut by a horizontal plane gives us a circle.

Example 7, Aishah Amri – Vaia Originals

Euler’s Formula

Euler’s Formula states that for any polyhedron that does not intersect itself or have any holes, the number of faces plus the number of vertices minus the number of edges always equals two. This can be written by the expression below.

Let us look at an example that applies this formula.

Verify that Euler’s Formula is satisfied for a square pyramid.

Solution

From our table above, a pyramid has the following features:

Number of Faces: 5

Number of Vertices: 5

Number of Edges: 8

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