In this lesson, we will certainly learn how to identify and describe two-dimensional numbers known as cross-sections that an outcome from slicing three-dimensional figures. In various other words, you deserve to slice a three-dimensional number (rectangular prism, pyramid, cone, cylinder, and also sphere) to present a two-dimensional see (rectangle, square, triangle, circle, trapezoid…). The two-dimensional check out is referred to as a cross-section.

You are watching: Cross section of a square pyramid

Let us start with a form that many of you have actually seen before – a cake! Think about it. Go you recognize that many cakes room shaped favor cylinders? Look at the cake below. It shows up to be round on top however what happens when you cut yourself a slice?

Can you see the rectangle ~ above the inside? as soon as you slice a cake the is the very same as a cross-section. The cross-section is merely a watch of the inside of a three-dimensional number after it is sliced. In mathematics, we shot to visualize plane cutting across the three-dimensional figures. There are several ways to cut a three-dimensional number that remainder on a base:

Cutting 3D figures
parallel to its basic (the shape will be the shape of the base)

perpendicular come its base

tilted away from that base

Example 1

Let us look at a rectangle-shaped prism.

As that rests ~ above its rectangle-shaped base, we cut it v a plane Parallel to that base. The cross-section is shaped choose a rectangle. It has the same shape and size as the base.

Now, we will certainly slice it through a airplane perpendicular to the base. Remember, perpendicular lines crossing the base at ninety degrees. Again, the cross-section is shaped like a rectangle. However, this time it has the same shape and size as another face that the prism.

Think around slicing the prism v a aircraft tilted far from that is base. This time, the cross-section will be shaped prefer a parallelogram.

Example 2

Another example of a cross-section would certainly be one that is created when we part a cone v its vertex. The course, the cone sits on its one base. If you reduced it perpendicular to its base and through its vertex, the cross-section would certainly be shaped favor an isosceles triangle. The basic of the triangle will be the basic of the cone.

The cone would produce a circle form if the plane sliced the parallel to its base

Example 3

Next, let’s photo a three-dimensional figure that has one base shaped prefer a polygon (a plane figure with at least three straight sides and angles) and also the other deals with shaped prefer triangles that share a usual vertex. Have the right to you guess: v what this is?

A pyramid is called for the shape of its base. Let us look in ~ a square pyramid (has a square base). Imagine a vertical airplane cutting v the pyramid perpendicular to the base. The cross-section would certainly be shaped prefer a triangle. If girlfriend sliced the pyramid parallel come the base, the cross-section would certainly be shaped choose a square (base). Now, reduced the pyramid perpendicular to the base, but NOT at the vertex. This will offer you a trapezoid!

Remember! When girlfriend slice any shape parallel to its base, girlfriend will ALWAYS get a number that is the form of the base.

Watch the videos to see some interactive instances of different varieties of cross-sections that deserve to be created from cubes and also pyramids.

Match the Slice with the form Practice

Match the description to the shape.

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Slice a rectangular prism parallel to its base.Slice a cube perpendicular to its base.Slice a hexagonal pyramid through its vertex perpendicular come its base.Slice a square pyramid perpendicular to the base and also not through the vertex.Slice a cylinder parallel to its base.Slice a cube contempt tilted no horizontal no one vertical come the faces.