Surface Area
	When done with this lesson, you will be able to find the surface area of prisms, pyramids, and cylinders given dimensions. find a dimension of a prism, pyramid, or cylinder when given the surface area and other dimensions. explain how changes in one dimension affect the surface area of a prism, pyramid, or cylinder.
	Approximate completion time: 3 hours

You likely have studied surface area to some extent before this course.
With that in mind, let's dive into areas of surfaces of 3D shapes.

To help us understand each other clearly, please complete the following table of definitions in a new word document. (Keep it handy for your assignment.)

Use your online research skills for help.

Name	Description/Definition	Picture
cylinder
cone
prism
pyramid
rectangular prism
triangular prism
rectangular pyramid
edge
vertex
face

 

As you likely saw in your research, there are tons of different 3D shapes and names.
Did you find anything like these?

These are called "Stellated Polyhedra".

For fun you may wish to build your own polyhedron. Go for it!

 

	For starters, why don't you try to imagine how to create a cube. Visit this fabulous interactivity and try your imagination out.
	When you're ready for visualizing more 3D shapes, check out this fun activity.

 

In the midst of the fun, be sure to get the main idea: surface area is the area of all of the surfaces of a 3D shape.
The total area of all of the triangles, squares, circles, etc. that are the faces of the space figure is the surface area.

Many people like to think of surface area in terms of painting.
A painter will paint the walls of a room—that's surface area.
A painter's bucket is filled with paint—that's volume.

For example,

	Ian knows one gallon of paint will cover approximately 400 ft2. The room he is going to paint is rectangular, 8 feet tall, 12 feet wide and 10 feet long. Without painting the ceiling or floor, approximately how many cans of paint will he need for a single coat of paint? (Ignore the areas of the windows and doors as they can offset the waste in paint on the bucket, brush, rollers, etc.)
Solution:	First a drawing Then the "exploded" view of all the faces. The area of the four walls is 8·(12 + 10 + 12 + 10) = 8·44 = 352 square feet. Thus Ian should only need one can of paint.

 

Keep in mind that to find surface area of a 3D figure, you must calculate the area of each face.
Drawing an "exploded" view of the figure can be extremely helpful.

Now it's your turn to try your hand at some practice and some deep thinking problems in Assignment 8.02.