# Ch 11: Explorations in Core Math Geometry Chapter 11: Spatial Reasoning

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Spatial Reasoning chapter of your textbook.
- Watch fun videos that cover the spatial reasoning concepts you need to learn or review.
- Complete the quiz after watching each video lesson 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.

## Chapter Topics

You'll learn all of the geometry topics covered in the textbook chapter, including:

- Examples of cross sections
- Generating three-dimensional figures with rotations
- What are cylinders, pyramids, cones and spheres
- Finding the area and volume of shapes

*Explorations in Core Math is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Cross Section: Definition & Example

This lesson will define cross sections. We will look at famous types of cross sections called conic sections, how cross sections show up in the world around us, and how the study of these is useful in various real world scenarios.

### 2. Using Rotations to Generate Three-Dimensional Figures

Did you know that all you need is an arc to make a sphere? And all you need to make a cylinder is a line! Learn how this is possible by spinning these lines and curves around a central axis in this lesson.

### 3. Prisms: Definition, Area & Volume

Recognized by their base shape, prisms are objects that are three-dimensional and have straight parallel sides, top, and bottom. Discover more about prisms, including their measurements and how to find the surface area and volume.

### 4. Cylinder: Definition, Surface Area & Volume

In geometry, the shape of a soda can is an example of a cylinder. Learn how to define cylinders and the formulas used to measure a cylinder's surface area and volume.

### 5. Pyramids: Definition, Area & Volume

In geometry, pyramids are defined as three-dimensional objects with a polygonal base and sides that meet at the same point at the top, which is called the apex. Learn to identify and define pyramid shapes and how to measure their surface area and volume.

### 6. Cones: Definition, Area & Volume

A cone is defined as a three-dimensional object with a flat base and a single curved side that comes to a point at the top. Learn the formulas for measuring this shape, including surface area and volume.

### 7. Volume & Surface Area of a Sphere

The volume and surface area of a sphere can be calculated when the sphere's radius is given. Learn about the shape sphere and its radius, and understand how to calculate the volume and surface area of a sphere through some practice problems.

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### Other Chapters

Other chapters within the Explorations in Core Math - Geometry: Online Textbook Help course

- Explorations in Core Math Geometry Chapter 1: Foundations for Geometry
- Explorations in Core Math Geometry Chapter 2: Geometric Reasoning
- Explorations in Core Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Explorations in Core Math Geometry Chapter 4: Triangle Congruence
- Explorations in Core Math Geometry Chapter 5: Properties and Attributes of Triangles
- Explorations in Core Math Geometry Chapter 6: Polygons and Quadrilaterals
- Explorations in Core Math Geometry Chapter 7: Similarity
- Explorations in Core Math Geometry Chapter 8: Right Triangles and Trigonometry
- Explorations in Core Math Geometry Chapter 9: Extending Transformational Geometry
- Explorations in Core Math Geometry Chapter 10: Extending Perimeter, Circumference and Area
- Explorations in Core Math Geometry Chapter 12: Circles
- Explorations in Core Math Geometry Chapter 13: Probablity