About This Chapter
How It Works
- Identify the lessons in this textbook chapter with which you need help.
- Find the corresponding video lessons within this online chapter.
- Watch fun videos that cover the volume topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
You'll learn all of the geometry topics covered in the textbook chapter, including:
- The definition of polyhedron and planes
- Characteristics and types of platonic solids
- How to calculate the volume and area of prisms, spheres, cones, pyramids and cylinders
- Determining volume of an object using displacement
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. 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.
5. 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.
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. Volume of Cylinders, Cones, and Spheres
In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.
8. Volume of Prisms and Pyramids
In this lesson, we'll learn about prisms and pyramids. We'll look at the different types of prisms and pyramids, as well as practice calculating volume for each shape.
9. Using Displacement to Calculate the Volume of an Object
Determining the volume of an object is easy if that object is uniform and has a regular shape. For objects that are irregularly shaped, using the edges is not so straightforward, so instead we can measure the volume by displacement.
10. 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 Discovering Geometry An Investigative Approach: Online Help course
- Discovering Geometry Chapter 1: Introducing Geometry
- Discovering Geometry Chapter 2: Reasoning in Geometry
- Discovering Geometry Chapter 3: Using Tools of Geometry
- Discovering Geometry Chapter 4: Discovering and Proving Triangle Properties
- Discovering Geometry Chapter 5: Discovering and Proving Polygon Properties
- Discovering Geometry Chapter 6: Discovering and Proving Circle Properties
- Discovering Geometry Chapter 7: Transformations and Tessellations
- Discovering Geometry Chapter 8: Area
- Discovering Geometry Chapter 9: The Pythagorean Theorem
- Discovering Geometry Chapter 11: Similarity
- Discovering Geometry Chapter 12: Trigonometry
- Discovering Geometry Chapter 13: Geometry as a Mathematical System