Connecting Geometry©

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:

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.


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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