Geometry
Chapter 7, Similarity
Scale models play huge roles in movies. Spaceships featured in the Star Wars movies have become very popular with model builders. However, at times, the scale is unclear because the size of the actual ship was never known. The actual ships you see on the screen were models themselves! Below you will explore the actual dimensions and model dimensions of an X-wing fighter, the starfighter Luke Skywalker piloted when he destroyed the Death Star in Star Wars: A New Hope.
Part A, Changing the Size of Figures and
Part B, Similar Polygons
1.Go to the Star Wars ships Web site to see statistics for various starships featured in the Star Wars movies.
a. What is the length of the T-65B X-wing fighter?
b. If 1 meter = 3.2810 feet, what is the length of the X-wing in feet? In inches?
2. Go to Star Wars Lego Designs Web site to see a model of an X-wing starfighter.
a. Use this model to approximate the ratio of the length of the X-wing to its width.
b. Based on the information from 1b and 2a, what is the approximate width of the X-wing starfighter in feet? In inches?
3. Now, go to the Star
Wars model site to see listings for various Star Wars
models. Scroll down to MD-SW-7, the 3-piece Fighter set.
a. How long is the X-wing fighter model?
b. Assuming that this model is similar to the actual X-wing fighter, use the ratio of length to width you found in 2a to find the width of this X-wing fighter model?
c. What is the similarity ratio of the actual fighter to the model?
d. Show that this ratio is the same for the ratios of the lengths and the ratios of the heights.
e. What will be the relationship between the angles made by the wings in the X-wing model and the actual X-wing fighter?
Part C, Areas and Perimeters of Similar Polygons
4. Test your knowledge of surface area.
a. What is the ratio of the surface area of the X-wing fighter to the surface area of the model?
b. If it takes 0.75 cups of paint to cover the outside of the model, how many cups of the same paint would it take to cover the actual X-wing fighter?