3D Shapes Overview

TipLearning Objectives

By the end of this lesson, you’ll be able to:

  • Identify common three-dimensional figures and their components.
  • Distinguish between faces, edges, and vertices.
  • Relate nets to the 3D solids they form.
  • Recognize which formulas apply to which shapes.

Key Ideas

Three-dimensional figures have volume and surface area.
Common solids:

Shape Key Features Notes
Prism Two parallel, congruent bases; rectangular faces between Named by the base shape (e.g., triangular prism)
Pyramid One base; triangular faces meet at a vertex Also named by base shape
Cylinder Two circular, parallel bases Curved surface
Cone One circular base; curved surface meets at apex
Sphere No faces or edges Perfectly symmetrical

Components:

  • Face: flat surface
  • Edge: segment where faces meet
  • Vertex: point where edges meet
  • Net: 2D layout that can fold into the 3D shape

Basic 3D solids: prism, triangular prism, square pyramid, cylinder, cone, and sphere.

Nets for a cube, triangular prism, and square pyramid.

Common Problem Types

Identifying Shapes from Nets

Students match a 2D net to a 3D solid.
Example: Six equal squares → cube.

Counting Faces, Edges, Vertices

Example: A rectangular prism has
- 6 faces
- 12 edges
- 8 vertices

Determining Base Shape

Example: A prism with triangular ends → triangular prism.

Cross-Sections

Slicing solids creates different 2D shapes.
Example: Horizontal cut through a sphere → a circle.

Matching Shapes to Formulas

Identify whether a shape uses prism formulas, cylinder formulas, sphere formulas, etc.

Strategies

  • Identify the base—it determines the formula.
  • Visualize rolling out the shape into a net.
  • Count systematically (e.g., opposite faces in pairs).
  • Label drawings if needed.

Worked Examples

Example 1

A net consists of 4 rectangles in a row and two congruent triangles.
→ Shape: Triangular prism.

Example 2

How many edges does a square pyramid have?
Base has 4 edges + 4 edges to the apex → 8 edges.

WarningCommon Mistakes
  • Mixing up prisms and pyramids.
  • Forgetting that cylinders and cones have curved surfaces (not faces).
  • Counting faces/edges/vertices inconsistently.
  • Confusing base area with surface area.

Practice Problems

  1. What 3D shape has 6 faces, all rectangles?
  2. A net has one square and four triangles. What shape is formed?
  3. How many vertices does a triangular pyramid have?
  4. What is the shape of a cross-section of a cylinder cut vertically?
  1. Rectangular prism
  2. Square pyramid
  3. 4 vertices
  4. Rectangle

Summary

  • 3D shapes have faces, edges, and vertices.
  • Prisms have two parallel bases; pyramids have one.
  • Cylinders, cones, and spheres have curved surfaces.
  • Nets help visualize solids.
  • Name prisms/pyramids by their base shape.
  • Think in pairs when counting faces/edges.
  • Use nets to understand surface structure.