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# Chapter 11: Surface Area and Volume

Difficulty Level: At Grade Created by: CK-12

## Introduction

In this chapter we extend what we know about two-dimensional figures to three-dimensional shapes. First, we will determine the parts and different types of 3D shapes. Then, we will find the surface area and volume of prisms, cylinders, pyramids, cones, and spheres. Lastly, we will expand what we know about similar shapes and their areas to similar solids and their volumes.

Chapter Outline

## Summary

This chapter presents three-dimensional geometric figures beginning with polyhedrons, regular polyhedrons, and an explanation of Euler's Theorem. Three-dimensional figures represented as cross sections and nets are discussed. Then the chapter branches out to the formulas for surface area and volume of prisms, cylinders, pyramids, cones, spheres and composite solids. The relationship between similar solids and their surface areas and volumes are explored.

### Chapter Review

Match the shape with the correct name.

1. Triangular Prism
2. Icosahedron
3. Cylinder
4. Cone
5. Tetrahedron
6. Pentagonal Prism
7. Octahedron
8. Hexagonal Pyramid
9. Octagonal Prism
10. Sphere
11. Cube
12. Dodecahedron

Match the formula with its description.

1. Volume of a Prism - A. \begin{align*}\frac{1}{3} \pi r^2 h\end{align*}
2. Volume of a Pyramid - B. \begin{align*}\pi r^2 h\end{align*}
3. Volume of a Cone - C. \begin{align*}4 \pi r^2\end{align*}
4. Volume of a Cylinder - D. \begin{align*}\frac{4}{3} \pi r^3\end{align*}
5. Volume of a Sphere - E. \begin{align*}\pi r^2+ \pi rl\end{align*}
6. Surface Area of a Prism - F. \begin{align*}2 \pi r^2+2 \pi rh\end{align*}
7. Surface Area of a Pyramid - G. \begin{align*}\frac{1}{3} Bh\end{align*}
8. Surface Area of a Cone - H. \begin{align*}Bh\end{align*}
9. Surface Area of a Cylinder - I. \begin{align*}B+\frac{1}{2} Pl\end{align*}
10. Surface Area of a Sphere - J. The sum of the area of the bases and the area of each rectangular lateral face.

### Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9696.

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Date Created:
Aug 09, 2013
Last Modified:
Aug 04, 2016
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