### Unit 10: Surface Area and Volume

Finding the amount of space inside of an object is important, and something you will do in your everyday life. If you try to fill a box with DVDs, to fill up a sandbox, or to fill a pool with water, you will use concept of volume. There are more shapes than just simple boxes, so you will learn to find the amount of space inside different types of three-dimensional objects.

Finding the amount of space on the outside of an object is also something you will do in your everyday life. If you decide to paint your house, you need to know how much space is going to be painted; buying too much paint would be a waste of money, and buying too little paint would be a nuisance. A few minutes of calculating can ensure that you get the amount of paint you need.

**Completing this unit should take you approximately 14 hours.**

Upon successful completion of this unit, you will be able to:

- find surface area and volume for prisms, cylinders, pyramids, cones, and spheres; and
- find surface area and volume of composite solids.

### 10.1: Polyhedrons

Read this section, which defines various terms associated with polyhedron. Then, complete the practice problems. These questions will provide you with the opportunity to apply properties of three-dimensional figures.

### 10.2: Representing Solids

Read this section, which defines various terms and methods associated with representing solids. Then, complete the practice problems. These questions will provide you with the opportunity to apply properties of representing solids.

### 10.3: Prisms

Read this section, which discusses the surface area and volume of prisms. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas for surface area and volumes of prisms.

### 10.4: Cylinders

Read this section, which discusses the surface area and volume of cylinders. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of cylinders.

### 10.5: Pyramids

Read this section, which discusses the surface area and volume of pyramids. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of pyramids.

### 10.6: Cones

Read this section, which discusses the surface area and volume of cones. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of cones.

### 10.7: Spheres

Complete this assessment, which tests your knowledge on surface area and volume. You can review the concepts associated with these questions with the content in subunits 10.3-10.7.

Read this section, which discusses the surface area and volume of spheres. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of spheres.

### 10.8: Composite Solids

Read this section, which discusses the surface area and volume of composite solids. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the formulas to find the surface areas and volumes of composite solids.