Suppose you build a cube whose length, width, and height are each 2 cm. What is the volume of this cube? What is its surface area? Repeat this procedure for a 3 x 3 x 3 cube and then for a 4 x 4 x 4 cube. What patterns do you notice? Can you predict the volume and surface area of a 17 x 17 x 17 cube? How about an s x s x s cube?
Find the volume of an irregularly shaped large object. First, find a small plastic model of that object – one that you wouldn’t mind getting wet (like a model of a dinosaur). Next, record the volume of the model using displacement. That is, fill a graduated cylinder about half-way with water and record the volume; then, completely submerge the model into the water and record the new volume. The volume of the model can be determined by subtracting the original volume from the new volume. Finally, find a scale factor between the model and the large object, and then use this scale factor and the model’s volume to compute the volume of the original object.