About This Chapter
High School Geometry: Geometric Solids - Chapter Summary and Learning Objectives
Geometry is used in various professions, like drafting, architecture, astronomy, medical imaging or graphic design. This chapter explores how planes and lines behave in space. You can learn to define and illustrate many platonic solids, including tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron. You can also meet many other geometric solids, learning to not only define and illustrate them, but also investigating the formulas for their surface areas, volumes or lateral areas. At the end of this chapter, you should be able to:
- Define a polyhedron and give examples
- Define and illustrate five types of platonic solids
- Define and illustrate a prism, pyramid, right circular cylinder, right circular cone and a sphere; explain how to calculate the surface area and volume of each, giving examples
- Discuss the formulas for lateral area of a pyramid, cylinder and cone
|Planes and the Polyhedron||In this lesson, you'll learn how lines and planes behave in space.|
|What Are Platonic Solids?||After watching this video, you'll be able to define and illustrate five major types of platonic solids.|
|Prisms||This lesson shows you how to define and calculate the area and volume of prisms.|
|Pyramids||Learn the methods for finding the area and volume of a pyrimid as well as the formula for lateral area of a pyramid.|
|What Are Cylinders?||This video lesson covers the calculation for the area and volume of a cylinder and the formula for lateral area of a cylinder.|
|Cones||We'll show you how to calculate area and volume of a cone and use the formula to find the lateral area of a cone.|
|Spheres||Learn how to calculate area and volume of a sphere.|
1. Planes and the Polyhedron: Definition and Example
Did you ever wonder what the pyramids in Egypt have to do with math? Watch this video to find out where in math a pyramid comes into play. Also, learn how flat, 2-dimensional shapes also come into play.
2. What Are Platonic Solids? - Definition and Types
Watch this video lesson, and you will learn that there are only five platonic solids in the whole world. You will also learn what they look like and see real-life examples.
3. Prisms: Definition, Area & Volume
Watch this video lesson and you will see that there are different kinds of prisms. You will also learn how to separate a prism into its various parts so you can easily find the surface area. You will also learn the formula for the volume.
4. Pyramids: Definition, Area & Volume
Do you think of the great pyramids of Egypt when you hear the word pyramids? Watch this video lesson to learn why they are called pyramids and also how to find their surface area and volume.
5. What Are Cylinders? - Definition, Area & Volume
Watch this video lesson to learn why soda cans are cylinders and the method by which you can discover how much soda can fit inside by finding the volume. You will also learn about finding a cylinder's surface area.
6. Cones: Definition, Area & Volume
Watch this video lesson to learn where in the real world you will see cones. Also, you will learn the formulas for finding the surface area and volume of these cones.
7. Spheres: Definition, Area & Volume
Watch this video lesson to learn how you can find the surface area and volume of spheres. Learn the formulas and measurements you need to solve problems and discover how to identify spheres in the real world.
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Other chapters within the Geometry: High School course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry