# Ch 33: Praxis Mathematics: Three-Dimensional Space and Volume

### About This Chapter

## Praxis Math: Volume - Chapter Summary

With the video lessons in the Volume chapter, you can refresh and update your knowledge of how to determine the volumes of various objects. This is some of the knowledge you'll need for the Praxis Math: Content Knowledge exam. In this chapter, you'll learn about:

- Cones: definition, area, and volume
- Cylinders: definition, area, and volume
- How to calculate the volumes of basic shapes
- How to measure volume
- Prisms: definition, area, and volume
- Pyramids: definition, area, and volume
- Solving applied problems involving volume
- Spheres: definition, area, and volume
- Volume and Cavalieri's principle
- Volume of cylinders, cones, and spheres
- Volume of prisms and pyramids

With video lessons that use clear language and examples, we can help make reviewing volume concepts simple and enjoyable.

### Praxis Math: Objectives

The Math Content Knowledge exam assesses your knowledge, abilities, and skill in mathematical problem solving, reasoning and proof, representation, connections, and use of technology to measure your readiness for teacher licensing in math. Whether you take the paper-delivered or the computer-delivered Praxis Math test, the test will have 50 multiple-choice questions that require a graphing calculator. The test includes approximately five geometry questions, making up about ten percent of the total exam. For the geometry portion of the exam, you should know how to calculate volumes of 2- and 3-dimensional figures as well as of regions and solids composed of these figures.

The self-assessment quizzes included with each video lesson help you to check your understanding of the information you've learned as you go. Quizzes also help you gain experience with the types of questions you find on the actual test.

### 1. Overview of Three-dimensional Shapes in Geometry

We are surrounded by three-dimensional shapes. Watch this video lesson to see what some three-dimensional shapes look like, such as a cube, a sphere, a brick, and a cylinder.

### 2. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

### 3. 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.

### 4. 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.

### 5. Ellipse: Definition, Equation & Examples

This lesson will cover the definition of ellipses and the standard form equation of an ellipse. It will also examine how to determine the orientation of an ellipse and how to graph them.

### 6. The Hyperbola: Definition, Vertices, Foci & Graphing

In this video lesson, we'll learn what a hyperbola is and how to graph one using the standard equation to find the center point, vertices and focus points.

### 7. How to Write the Equation of a Hyperbola in Standard Form

When it comes to equations in algebra, there is most always a standard form that provides us with useful information. Watch this video lesson to learn how to write the standard form equation of a hyperbola by using information about the hyperbola.

### 8. The Parabola: Definition & Graphing

Watch this video lesson to learn what a parabola is and how you can graph it. Find out how to extract useful information from the standard form equation of a parabola to help you graph it.

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### Other Chapters

Other chapters within the Praxis Mathematics - Content Knowledge (5161): Practice & Study Guide course

- Praxis Mathematics: Counting Numbers Properties
- Praxis Mathematics: Rational and Irrational Numbers
- Praxis Mathematics: Solving Problems with Reasoning
- Praxis Mathematics: Percents
- Praxis Mathematics: Ratios and Proportions
- Praxis Mathematics: Scientific Notation & Order of Magnitude
- Praxis Mathematics: Algebraic Expressions
- Praxis Mathematics: Algebraic Equations
- Praxis Mathematics: Algebraic Fractions
- Praxis Mathematics: Linear Equations
- Praxis Mathematics: Systems of Equations
- Praxis Mathematics: Radicals Operations
- Praxis Mathematics: Exponents
- Praxis Mathematics: Distance
- Praxis Mathematics: Functions
- Praxis Mathematics: Inverse Functions
- Praxis Mathematics: Logarithmic Functions
- Praxis Mathematics: Rational Functions
- Praxis Mathematics: Complex Numbers Operations
- Praxis Mathematics: Sequences, Series & Probability
- Praxis Mathematics: Combinations & Permutations
- Praxis Mathematics: Quadratic Equations
- Praxis Mathematics: Polynomials
- Praxis Mathematics: Matrix Algebra
- Praxis Mathematics: Algebraic Formulas
- Praxis Mathematics: Measurement
- Praxis Mathematics: Area
- Praxis Mathematics: Polygons
- Praxis Mathematics: Quadrilaterals
- Praxis Mathematics: Circles
- Praxis Mathematics: Triangles
- Praxis Mathematics: Congruence, Similarity and Transformations
- Praxis Mathematics: Data
- Praxis Mathematics: Distributions
- Praxis Mathematics: Graphing
- Praxis Mathematics: Trigonometry
- Praxis Mathematics: Continuity
- Praxis Mathematics: Asymptotes
- Praxis Mathematics: Limits
- Praxis Mathematics: Derivatives
- Praxis Mathematics: Integrals
- Praxis Mathematics: Optimization and Differentiation
- Praxis Mathematics: Theorems
- Praxis Mathematics: Statistics
- Praxis Mathematics: Interpreting Statistics
- Praxis Mathematics: Understanding Logic
- Praxis Mathematics: Content Knowledge Flashcards