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Describe 2D Cross-Sections of 3D Figures

Students visualize and describe the two-dimensional figures that result from slicing three-dimensional figures (prisms, pyramids, cones, cylinders, and spheres) with a plane. They identify the shape of each cross-section and explain how the angle of the cut affects the shape.

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Describe 2D Cross-Sections of 3D Figures

Grade 7 · Geometry · question 1 of 3

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20 rungs. A star at the top.

Hold the chest and cut level. Pick the cross-section.

Choose the shape of the slice.

How it is taught

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A cross-section is the 2D face made by a flat cut.

A cut parallel to the base copies the base's outline.

A box's base is a quadrilateral.

Read it: Cross sections

Slice a cylinder parallel to its base and the cut face is a circle, the same shape as the base.

  1. Find the solid's base.
  2. A cut parallel to the base has the same shape as the base.
  3. Name that shape: it is the base's own shape.

A prism or a cylinder is the same all the way along, so every cut parallel to its base is a copy of the base.

A pyramid or a cone narrows toward its top, so a cut parallel to its base is the base's shape, only smaller.

A box or a square pyramid has a four-sided base, so its parallel cut has four sides too.

A cut parallel to the base has the same shape as the base.

Naming the side seen from the front: a rectangle.

The cut runs parallel to the base, so it is a circle, like the base.

A rectangular prism is cut parallel to its base. Name the shape of the cut face: circle, triangle or quadrilateral. — quadrilateral. A cut parallel to the base copies the base, a rectangle, a quadrilateral.

Slicing a square pyramid

When we slice a 3D shape with a flat cut, the new face we see is called a cross-section. Let's try it!

Here's a square pyramid — a square base with four triangle faces meeting at the top.

Grade 7 · How a slice turns a 3D shape into a 2D shape

First, let's slice it flat across, parallel to the base.

Our slicing plane goes straight through, all at the same height.

The cross-section is a square — every horizontal slice gives us a square.

Now let's slice straight down, right through the top point.

This plane runs from the apex all the way to the base.

This time the cross-section is a triangle!

Same pyramid — a flat slice gave a square, a vertical slice gave a triangle. The angle of the cut decides the 2D shape.

Now you try. Count the flat faces of this solid. How many flat faces?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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