3D Geometry Cross Sections & Solids of Revolution

Duke, Susan Barnhouse, DavidK, May 6, 2026

3D Geometry: Cross Sections & Solids of Revolution

Table of Contents

  1. Cross Sections of 3D Solids
    1. Sections of Rectangular Prisms
    2. Sections of Triangular Prisms
    3. Sections of Rectangular Pyramids
    4. Sections of Triangular Pyramids
    5. Sections of Cylinders
    6. Sections of Cones
    7. Sections of Spheres
  2. Cross Sections from three Points
    1. Cube Cross Sections
    2. Cross Section of a Cone
    3. Cross Section of a Cylinder
    4. Cross Section of a Sphere
    5. Exploring Sections of Cubes
  3. Cross Sections Simple
    1. section of cone
    2. section of sphere
    3. cutting a sphere
  4. Adjustable Cross Sections
    1. 3D View - Cross Section of a Prism Intersected by a Plane
  5. Solids of Revolution
    1. Solid-of-Revolution
    2. Sphere created from Revolution
    3. Truncated Cone created from Revolution
    4. Custom Made Solid of Revolution
  6. Solids of Revolution Hollow
    1. Solids of Revolution with Adjustable Axis
    2. Solids of Revolution with Adjustable Axis Hollow Cylinder
    3. Solids of Revolution

1.

Cross Sections of 3D Solids

Use these worksheets to gain experience with the cross sections and solids.

  • 1. Sections of Rectangular Prisms
  • 2. Sections of Triangular Prisms
  • 3. Sections of Rectangular Pyramids
  • 4. Sections of Triangular Pyramids
  • 5. Sections of Cylinders
  • 6. Sections of Cones
  • 7. Sections of Spheres

1.1.

Sections of Rectangular Prisms

Drag the blue points to see the different sections of the rectangular prism (cuboid).
Anthony Or. GeoGebra Institute of Hong Kong
How many different shapes can you make?
What cross section have you made?[br]Please spin the figure around.
– DavidK, Anthony OR 柯志明

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2.

Cross Sections from three Points

  • 1. Cube Cross Sections
  • 2. Cross Section of a Cone
  • 3. Cross Section of a Cylinder
  • 4. Cross Section of a Sphere
  • 5. Exploring Sections of Cubes

2.1.

Cube Cross Sections

Move the points I, K, and J around on the edges of the cube.
1) What are the different cross section shapes that you can make?[br]2) What is the cross section with the least number of sides?[br]3) What is the cross section with the most number of sides?[br]4) Can you make any regular polygonal cross sections? How would you position the points for each?
– Edward Knote

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3.

Cross Sections Simple

  • 1. section of cone
  • 2. section of sphere
  • 3. cutting a sphere

3.1.

section of cone

The cross section of a cone is shown in detail. The cone has base radius equal to its height. [br]Drag the red dot to change the height of the cutting plane (which is h).[br]The section is a circle of radius a. Its area can be found in terms of h. [br]Drag F to turn the marked triangle if needed.
section of cone
– Arthur Lee

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4.

Adjustable Cross Sections

  • 1. 3D View - Cross Section of a Prism Intersected by a Plane

4.1.

3D View - Cross Section of a Prism Intersected by a Plane

Examine the intersection of a plane and a prism. What kind of cross sections you can get?

What are the least amount of sides in your polygon cross section? What are the most sides you can get in a cross section?
– Azucena Overman

5.

Solids of Revolution

  • 1. Solid-of-Revolution
  • 2. Sphere created from Revolution
  • 3. Truncated Cone created from Revolution
  • 4. Custom Made Solid of Revolution

5.1.

Solid-of-Revolution

– Samir Shrestha

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6.

Solids of Revolution Hollow

The 2D solid is not touching the axis of revolution.

  • 1. Solids of Revolution with Adjustable Axis
  • 2. Solids of Revolution with Adjustable Axis Hollow Cylinder
  • 3. Solids of Revolution

6.1.

Solids of Revolution with Adjustable Axis

– DavidK

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