About This Chapter
Three-Dimensional Geometry - Chapter Summary
In geometry, learning how to visualize problems can often win you 'half the battle'. This chapter can show you how to pull out all the important details, diagram those essential pieces to use as a key to a real problem and then make sure that your answer fits all the original details.
The lessons go over the steps of calculating volumes for basic shapes, such as pyramids, prisms, spheres, cylinders and cones. You can also practice discovering surface area and three-dimensional coordinates. All of the following topics appear in this chapter:
- Visualization in geometry problems
- Methods for calculating volume of shapes that have the same cross-section from top to bottom
- Additional rules needed to calculate volumes for shapes that don't have the same cross-section
- Formulas used to find the surface area of three-dimensional shapes
- Calculation of coordinates in three dimensions
- Application of scale factors to area, perimeter and volume
Each lesson is led by an experienced instructor and includes a video, a text record of what's being said in the video and a short, multiple-choice quiz. If you want to review a certain topic on a video, you can click on the timeline to expose the handy video tags that help you target just the right portions. Some lessons also contain links to additional text-only lessons that can provide even more clarification on select topics. You can also use the multiple-choice quizzes to get comfortable with the style of questions you'll see on the SAT subject test.
Three-Dimensional Geometry Objectives
The concepts learned in this chapter can help you prepare for the SAT Subject Test Math 2, which assesses your mastery of advanced math techniques. Add the results from this test to your admissions materials and potentially earn college credit from the college of your choice. Three-dimensional geometry concepts are tested in the geometry and measurement content area of the test, which represents 28%-32% of the entire test. Within that content area, 4%-6% of the test questions focus on three-dimensional geometry. In addition to geometry and measurement, this subject test has 50 multiple-choice questions on numbers and math operations, algebra, functions, data analysis and probability.
1. How to Solve Visualizing Geometry Problems
A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.
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. What is Surface Area? - Definition & Formulas
In this lesson, you use general and specific formulas to learn how to find the surface area of three-dimensional shapes, such as cubes, prisms, spheres, cones and cylinders.
6. How to Plot Points in Three Dimensions
In this lesson, we'll look at what a three-dimensional coordinate system looks like. After that, we'll learn how to plot points in three dimensions and look at a couple of examples of the process.
7. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.
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Other chapters within the SAT Subject Test Mathematics Level 2: Practice and Study Guide course
- Structure & Strategies for the SAT Math Level 2
- Basic Math Review
- Square Roots
- Basic Algebraic Expressions
- Algebraic Linear Equations & Inequalities
- Algebra: Absolute Value Equations & Inequalities
- Algebra: Polynomials
- Functions in Math
- Algebra: Rational Expressions
- Understanding Sequences & Series
- Understanding Exponentials & Logarithms
- Complex and Imaginary Numbers
- Coordinate Geometry Basics
- Coordinate Geometry: Graphing Linear Equations & Inequalities
- Advanced Coordinate Geometry
- Overview of Trigonometry
- Probability, Combinations & Permutations
- Working with Data & Statistics
- Basic Mathematical Logic
- Limits of Functions
- SAT Subject Test Mathematics Level 2 Flashcards