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Cross Sections

Cross Sections. What you see when you slice. What is a Cross Section?. So far we have dealt with two-dimensional figures and three-dimensional figures independently (more or less), but cross sections are where the two shall meet.

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Cross Sections

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  1. Cross Sections What you see when you slice.

  2. What is a Cross Section? • So far we have dealt with two-dimensional figures and three-dimensional figures independently (more or less), but cross sections are where the two shall meet. • A cross section is the two-dimensional figure that results or that is revealed when a two-dimensional plane intersects with a three-dimensional figure.

  3. Huh? • Everybody say “What”. • “What !” • Put a little better, it is the shape you see on the inside when you slice off a piece of a figure.

  4. Cutting an orange in half is a good example. When you slice the orange in half and then look at the new face you just made, what is its shape? A Circle!

  5. Cross Sections all Around • Cross Sections are all around us, everywhere. • There is a cross section when you cut your birthday cake. • There are cross sections in every loaf of sliced bread. • A floor plan of a house is nothing but a fancy cross section. • Science books and advertisements are full of them.

  6. Cross Sections and more Cross Sections • Cross sections let us see what is on the inside. • X- rays are good examples. • Mall maps are too. • Can you think of some examples of cross sections that you have seen and how or why they are used?

  7. There’s more than One Way to slice a Figure. • There is an infinite number of ways that a two-dimensional plane can intersect with a three-dimensional figure, but since we don’t have time to discuss them all, we’re going to stick with following for today: • Intersections Parallel with the base. • Intersections Perpendicular with the base.

  8. What is the base of a three-dimensional figure? The closed plane figures that are connected to either a second parallel base or to a vertex to form a three dimensional figure. Base Vertex

  9. What does that mean? • An intersection perpendicular to the base will be exactly straight up and down have 900 angles where the two-dimensional plane meets the three-dimensional base. • Now do you remember what perpendicular is? 90 degrees

  10. What does that mean? • An intersection parallel to the base is a side to side cut that is parallel to the base of the three-dimensional figure. It will always yield a two-dimensional figure in the shape of the base. • Remember:Parallel means that if the two-dimensional plane and the base of the figure went on forever, they would never, ever touch (intersect).

  11. A Cross Section Parallel to the base of a Cylinder gives us what two- dimensional shape? A Circle

  12. A Cross Section Perpendicular to the base of a Cylinder gives us what two- dimensional shape? A Rectangle

  13. A Cross Section Perpendicular to the base of a Pyramid gives us what two- dimensional shape? A Triangle

  14. A Cross Section Parallel to the base of a Square Pyramid gives us what two- dimensional shape? A Square

  15. A Cross Section Perpendicular to the base of a Rectangular Prism gives us what two- dimensional shape? A Rectangle

  16. A Cross Section Parallel to the base of a Rectangular Prism gives us what two- dimensional shape? A Rectangle

  17. A Cross Section Perpendicular to the base of a Cone gives us what two-dimensional shape? A Triangle

  18. A Cross Section Parallel to the base of a Cone gives us what two-dimensional shape? A Circle

  19. Finally, no matter how you slice it, the cross section of a sphere is going to be a …. A Circle

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