Chapter 12

Volume and Surface Area

Wherever you look around you, you see 3-dimensional shapes: buildings, furniture, plants, people themselves: all are solid objects with height, width and depth. When we draw any object, we have the choice of drawing it "flat" (2-dimensionally) or as a "solid" (3-dimensionally). The floor plan you drew in the previous chapter is an example of a 2-dimensional representation of a house. Architects often draw 3-D drawings of houses, so their client can more clearly understand what the house will look like when it is built. In this chapter, you will be studying 3-dimensional objects such as cubes, cylinders and pyramids, and learning how to draw them so that they do appear to be 3-D. Some examples of the 3-D solids you will be studying are drawn below:

Once you know how to draw these solids, you can combine them to draw all sorts of 3-dimensional objects, such as furniture, houses, and even castles! The photograph below is a castle called Laussel, at Marquay, in the Perigord region of France.

This beautiful photo came from a fascinating website with images and information about many castles. If you would like to visit this website, click on the link below:

http://fox.nstn.ca/~tmonk/castle/images.html

This and many other castles are made up of geometric solids. Can you find prisms, pyramids, cones and cylinders in the photograph? You can draw castles using a combination of these geometric solids. An example of a simple castle, drawn in Adobe SuperPaint, is shown below:

Here is another example of a castle. This castle was constructed in perpsective, using the Geometer's Sketchpad. You can construct castles using a compass and ruler, or on tracing paper over a grid.

Project

Do some research on the net, and find some other images of castles. Read some information about the castles, and explore any aspects that interest you. Then design and create a 3-D drawing of your own castle, using geometric solids. It would be best to draw on a piece of tracing paper over a perspective grid, which you can print from the following web page: 2 Point Perspective Grid

You must have at least one each of the four solids we have studied: Prism, pyramid, cylinder, cone. Then find the volume of the solid portions of your castle. Be sure to write all formulas, and show all your work!

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