1. Cross sections of 3-D solids

2. Cross Sections
A section of a tree trunk is roughly in the shape of a cylinder as shown.
When a tree trunk is cut in order to see the tree rings, a cross section of the trunk is being studied.

3. Cross section – the part of a solid cut by a plane
Suppose a plane intersects a cylinder parallel to its bases. What is the shape of the cross section? Sketch an example.

5. Suppose a plane intersects a cylinder perpendicular to its bases so that the plane passes through the centers of the bases. What is the shape of this cross section? Sketch an example of this cross section.

7. The cylinder below sits on a horizontal base
The cylinder below sits on a horizontal base. Draw and describe the cross-section formed when the cylinder is cut by a plane that is tilted away from its base.

8. The cross-section is shaped like an oval
The cross-section is shaped like an oval. In mathematics, this shape is called an ellipse.

9. Suppose a plane intersects a pyramid so that it is parallel/perpendicular to its base. What is the shape of this cross section? Sketch an example of this cross section.

10. Parallel to base

11. Perpendicular to base

12. The pyramid below has a square horizontal base
The pyramid below has a square horizontal base. Draw and describe the cross-sections formed when the cone is cut by a vertical plane that does not pass through the vertex at its top.

13. The cross-section will be shaped like a quadrilateral
The cross-section will be shaped like a quadrilateral. This figure is called an isosceles trapezoid.

14. Next let’s look at a rectangular prism, a cube, a cone, and a sphere.

15. Rectangular Prism

16. Cubes

17. Cones

18. Spheres

19. 1. The cylinder below is cut by the plane shown
1. The cylinder below is cut by the plane shown. What is the shape of the cross-section formed?
Circle
Rectangle
Trapezoid
Triangle

20. 2. The cube below is cut by the plane shown
2. The cube below is cut by the plane shown. What is the shape of the cross-section formed?
Circle
Rectangle
Square
Triangle

21. 3. Suppose a cone is cut by a plane
3. Suppose a cone is cut by a plane. Which cross-section is NOT possible?
Circle
Ellipse
Square
Triangle

22. 4. The cross-section of a three-dimensional figure is shaped like a circle. The three-dimensional figure could NOT be a ________.
Cone
Cylinder
Pyramid
Sphere

23. 5. A cylinder is cut by a plane to form a cross section shaped like an ellipse. How could the plane that formed the cross-section have cut the cylinder?
Parallel to a base of the cylinder
Perpendicular to a base of the cylinder
Slightly tilted away from a base of the cylinder
None of the above