An Extended Problem on Perimeter, Area, and Volume Suppose you have 10 separate unit cubes. The total volume is 10 cubic units and the surface area is 60 square units. If you arrange the cubes as shown, the volume is still 10 cubic units, but the surface area is only 36 square units. For each of the following problems, assume that all cubes are stacked to form a single shape sharing at least one complete face (no loose cubes allowed). a. What's the greatest possible surface area you can obtain with 10 cubes? Demonstrate the calculations you used to derive your answer. b. How can you arrange the 10 cubes to get the smallest possible surface area? Demonstrate the calculations you used to derive your answer. c. Biologists have found that an animal's surface area and volume are important factors in its regulation of body temperature. Select an animal from hot regions and an animal from cold regions, and discuss how their surface areas and volume are suited to their climates. Include pictures and explain how you concluded