Superlesson
Project 9-3
Geometry
Chapter 9, Surface Area and Volume
Collies look like bigger versions of Shetland Sheepdogs, otherwise known as Shelties. Below, you will use measurements for the bodies of each of these canines to explore whether these two animals truly have mathematically similar shapes.
Part A, Surface Area of Similar Solids
1. You will refer to two Web sites in this activity. The Web site which gives the breed standards for Collies and the Shetland Sheepdogs Web site.
a. For now, let's assume that the Collie and the Sheltie are mathematically similar. Use the average of the minimum and maximum heights at shoulder to find the similarity ratio between a female Collie and a Sheltie. Then, find the similarity ratio between a male Collie and a Sheltie.
b. Use these similarity ratios to find the ratio of the surface areas between a female Collie and a Sheltie. Then, find the similarity ratio between the surface areas of a male Collie and a Sheltie.
c. What does the surface area of an animal actually measure?
Part B, Volume of Similar Solids
3. You will now investigate whether the Sheltie is actually mathematically similar to either the female or male Collie. You will use the ratio of their weights to determine this. For this exercise, you can assume that the weight ratio and volume ratio are numerically equivalent.
a. Assuming the female Collie is mathematically similar to the Sheltie, what should the ratios of their weights be?
b. Given the weight of the Sheltie, about what should a female Collie weigh if they are mathematically similar?
c. Are a female Collie and a Sheltie mathematically similar?
d. Are a male Collie and a Sheltie mathematically similar? Why or why not?