Cross sections of 3-D solids

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.

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.

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.

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.

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

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.

Parallel to base

Perpendicular to base

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.

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.

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

Rectangular Prism

Cubes

Cones

Spheres

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

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

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

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

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