Fix the mistake: Solid Figures ①

Solid Figures ① Types and Names of Solids

Let us organize the types and names of solids, which are plane figures extended into space. Solids are broadly divided into polyhedra and solids of revolution.

Polyhedra

A solid enclosed only by flat faces (polygons) is called a polyhedron.

  • Prism: A prism with a polygon as its base and rectangles as its lateral faces (triangular prism, rectangular prism, hexagonal prism, and so on)
  • Pyramid: A solid with a polygon as its base and one vertex (triangular pyramid, rectangular pyramid, and so on)
  • Regular polyhedron: A solid whose faces are congruent regular polygons and where the same number of faces meet at each vertex (the five types are the regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron, and regular icosahedron)

Solids of Revolution

A solid formed by rotating a plane figure one full turn around a straight line (the axis of rotation) is called a solid of revolution.

  • Cylinder: A rectangle rotated (the base is a circle, and the lateral surface is curved)
  • Cone: A right triangle rotated
  • Sphere: A semicircle rotated
📘 Example ①
Name the following solids.
(1) A prism with a regular hexagon as its base and rectangles as its lateral faces
(2) A pyramid with a square as its base and one vertex
Answer:(1) Hexagonal prism　(2) Square pyramid (regular square pyramid)
💡 Key Points
  • Prism: polygonal base + rectangular lateral faces
  • Pyramid: polygonal base + one vertex
  • Solid of revolution: a plane figure rotated around an axis

Practice Problems

  1. Name the prism and pyramid that each have an equilateral triangle as their base.
  2. What kind of solid is formed when a rectangle is rotated one full turn around the axis of rotation?

Answers and Explanations

  1. Answer: The prism is a triangular prism, and the pyramid is a triangular pyramid.
  2. Answer: A cylinder. Rotating a rectangle around one of its sides produces a cylinder.

Math (Grade 7): related lessons