1.3 Surface area of 3-dimensional shapes

Your dad told you that he is going to have the house repainted next week. He asked you to help him. The first task was to find out how much paint you guys would need in order to paint the whole thing. Are you up for the challenge? Thanks to this chapter on surface area, computing for the approximate amount of paint that you need wouldn’t be that hard to figure out. But how do we know how the surface area of your house?

First off, we need to transform the 3-dimensional house into a 2-dimensional form by looking at its front, top, and sides. In the first part of this chapter, we will learn how to do just that. Note that the key to learning this quickly is either by effectively outlining the edges and vertices of the object or by using different colored pens to denote which sides are found in the top, front and side.


After figuring out the front, top and sides, you will then need to draw the net of the house to see the different shapes that comprise it, such as faces of a cube are in fact 6 squares, and a cylinder is made by a 2 circular bases and a rectangle. We will be able to learn how to do this at ease in the second part of this chapter. Apart from that we will also learn how to transform a net into a 3D shape. If you aren’t too good at drawing 3D objects, then you can learn how to draw 3D objects online.

After finding out all the faces, edges and vertices of your house, we move on to computing the combined area of these shapes. In the third section, we will be looking at how to find the surface are of prisms. We will focus on regular rectangular and triangular prisms.

For the rectangular prisms, we would need to use its width, length and height and plug these values in a formula. For the triangular prisms, we are going to use the same elements, adding the value for the side. If ever the value for the side, height and width are not given, we can use the Pythagorean Theorem to solve for it.

In the last part of this chapter, we will tackle the question of how to find the surface area of a cylinder by using the diameter or radius of the circle and the height of the cylinder.

Surface area of 3-dimensional shapes

In this section, we will learn how to calculate the surface area of 3D objects. We will also look further into the subject ? What would happen to the surface area if the shapes are cut into pieces? How about a piece is cut out of the shape?

Lessons

    • a)
      What are the dimensions of the cutout piece?
    • b)
      How does the surface area of the original rectangular object change after cutting out the corner piece?
  • 2.
    Below is a rectangular object formed by six blocks which all have the same size.

Teacher pug

Surface area of 3-dimensional shapes

Don't just watch, practice makes perfect.

We have over 4190 practice questions in College Algebra for you to master.