Cross-sections of three-dimensional figures

Learning Objectives Identify the two-dimensional shape created by the intersection of a plane and a three-dimensional figure. Describe how the angle and location of a slicing plane affect the shape and size of the resulting cross-section. Visualize and sketch the cross-sections of common solids like prisms, pyramids, cylinders, cones, and spheres. Calculate the area of a cross-section parallel to the base of a prism, cylinder, pyramid, or cone. Differentiate between horizontal, vertical, and oblique (angled) cross-sections. Apply the properties of similar figures to find the dimensions of cross-sections in pyramids and cones. Ever wonder how a CT scanner sees inside the human body or how a chef cuts a carrot into perfect circles? 🥕 You're already thinking about cross-s...

TermDefinitionExample Three-Dimensional Figure (Solid)An object that has three dimensions: length, width, and height. It occupies space.A cube, a sphere, a pyramid, or a cylinder. PlaneA flat, two-dimensional surface that extends infinitely in all directions. In this context, we think of it as a 'slicing' tool.The surface of a table, a wall, or a sheet of paper can be thought of as parts of a plane. Cross-SectionThe two-dimensional shape that is exposed when a plane intersects a three-dimensional figure.Slicing a cylindrical sausage horizontally results in a circular cross-section. Horizontal Cross-SectionA cross-section created by a plane that is parallel to the base of the 3D figure.A horizontal slice through a square pyramid creates a smaller square. Vertical Cross-SectionA c...

Prism/Cylinder Parallel Slice Rule A cross-section created by a plane parallel to the base of a prism or a cylinder is congruent to the base. Use this rule when a slice is made parallel to the top or bottom of a prism or cylinder. The area of the cross-section will be identical to the area of the base. Pyramid/Cone Parallel Slice Rule A cross-section created by a plane parallel to the base of a pyramid or a cone is a shape that is similar to the base, but smaller. Use this rule for slices parallel to the base of a pyramid or cone. The cross-section will be a scaled-down version of the base. You will often need to use properties of similar triangles to find its dimensions. Similar Figures Proportionality For a cone or pyramid, the ratio of the linear dimensions of the c...