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Cross Sections of 3D Shapes

HSG-GMD.B.4
Answer Keys Here

Aligned To Common Core Standard:

Geometric Measurement - HSG-GMD.B.4

What are Cross Sections of 3D Geometric Shapes? We all have seen shapes. They exist in different forms. Triangles, squares, rectangles, circles, rhombus, parallelograms, all are shapes. Just like us, shapes have different lengths, heights, and widths, as well. When a shape entails these three measurements, it is called a three-dimensional shape. For example, a square will have some measure of height, length, and width in it. Now let's take a look at another concept. What are cross-sections? Here we go: A cross-section is a shape we get when cutting straight through an object. For example, when we cut through a cylinder, the shape we will get is a circle. So, the cross-section of the cylinder is a circle. If you pretend that a shape is entirely made of butter or chesse and slice it with a knife, you have just created a cross section of that shape. They are a view inside the shape. Think about this the next time you cut vegetables to make a salad.

Printable Worksheets And Lessons


  • How's Your Eyes Step-by-step Lesson - Prior to the core curriculum, I always felt that they were missing a standard in most books on this.

  • Guided Lesson - This is a wonderful predictive skill to have. Look at this figure, if you were to see this object from the top, what would you see?

  • Guided Lesson Explanation - As far as explanations of this, it is hard to get unless you have a tactile 3D model, but I do my best.

  • Practice Worksheet - I as you to read and translate with the help of an arrow at step one. You will approach these 3D shapes from various perspectives.

  • Matching Worksheet - Match your perceived view to the object composition that is available on the chart.


Homework Sheets

It's amazing how students are lost when they first see these. Once they get it, it is simple for them.

  • Homework 1 - If we are looking at this object from the top, you will see the rectangle highlighted in this box.
  • Homework 2 - Cones and pyramids cones have one base. Cubes, prisms, and cylinders have two bases that are parallel and congruent.
  • Homework 3 - This isn't the shape you thought it was, at first. We work with hollow and solid shape fills.



Practice Worksheets

Saw a neat study on this skill. It seems Gen-X and younger are better at this skill than older generations.

  • Practice 1 - If you see this shape from the left, what would you see? Think about it in your mind.
  • Practice 2 - What would you view if these conditions were met. Yes, if you print this is full color there will be a dead giveaway.
  • Practice 3 - The pie piece will take a second to think about. We go through the entire thought process for you.



Math Skill Quizzes

Researchers cite the use of 3-D video games as being the reason younger generations are better at this skill.

  • Quiz 1 - These look like game pieces from Monopoly. See if you can visualize them in your mind.
  • Quiz 2 - Pay attention to where the arrow is pointed. Pretend that you were standing next to the shape and looking in the direction of the arrow.
  • Quiz 3 - Yes, number one is an open box. Why would you follow in that direction?


Where is This Skill Used in Real Life?

While we are spending a good deal of time on this topic hoping to better understand shapes, we need to realize the true nature and application of cross sections in everyday life. As is true with most things that are math related architectural engineers and construction managers rely on cross sections to better understand the structural integrity of the building they are creating or fixing up. Anyone that works with wood to build just about anything is constantly making cross sections on the wood they are cutting with the intent to make it suit a certain purpose. Geologist are sampling cross sectional portions of the Earth to determine past life and weather conditions. This technique is called coring. They will take long cylindrical samples of the Earth in portions. They then analyze each cross-sectional region to gain understanding as much as they can about the time period. Doctors use MRI technology to create computerized cross section images of our bodies to better understand aliments and injuries. This technology can clearly display a difference between healthy and diseased tissues.