About This Chapter
Geometric Solids - Chapter Summary and Learning Objectives
Flat shapes are cool, but an ability to work with geometric solids can take your math skills into a whole other dimension. Use the lessons in this chapter to learn how 2-D shapes, like triangles, squares and circles, can be used to form pyramids, prisms, spheres and other 3-D shapes. Instructors show you how to calculate their volume and area and introduce you to a special type of polyhedron known as a platonic solid. Lessons in this chapter are designed to teach you about the following:
- Properties of polyhedrons and platonic solids
- Formulas for finding the area and volume of geometric solids
- Characteristics of prisms, pyramids, cylinders, cones and spheres
|Planes and the Polyhedron: Definition and Example||Explore the 2-D surfaces of planes. Learn how they relate to polyhedrons, and get real-life examples of these shapes.|
|What Are Platonic Solids? - Definition and Types||Survey characteristics of tetrahedrons, cubes, octahedrons, dodecahedrons and icosahedrons.|
|Prisms: Definition, Area & Volume||Differentiate between triangular, square and pentagonal prisms. Calculate the surface area and volume for each type.|
|Pyramids: Definition, Area & Volume||Apply the formulas used to calculate the surface area and volume of square and triangular pyramids.|
|What Are Cylinders? - Definition, Area & Volume||Use the height of a cylinder and the radius of its base to determine surface area and volume.|
|Cones: Definition, Area & Volume||Enter a cone's height, the length of its side and the radius of its base into the formulas for surface area and volume.|
|Spheres: Definition, Area & Volume||Calculate a sphere's surface area and volume using the radius.|
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 NY Regents Exam - Geometry: Test Prep & Practice course
- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- Introduction to Geometric Figures
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Analytical Geometry
- Triangles and Congruency
- Parallel Lines and Polygons
- Conic Sections
- About the NY Regents Examinations
- NY Regents Exam - Geometry Flashcards