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Objectives: Calculate the surface area of a cube and a rectangular solid Explore how to increase the surface area of a cube while working within constraints Build a model of a cross section of the small intestine Calculate and compare the surface areas of folded and unfolded strips of tickets Discuss the relationship between surface area and absorption in the small intestine Read about what happens to undigested food and water in the large intestine Concepts: Nutrients pass through the walls of the small intestine by absorption. The amount of nutrients that pass into the bloodstream depends in part on the amount of surface area available for their absorption. Because humans must absorb large amounts of nutrients to support life activities, their digestive systems have a large surface area. The small intestine has folds, villi, and microvilli that increase its surface area. Excess water is absorbed into the bloodstream from the large intestine. Solid wastes are stored in the large intestine until they are eliminated from the body. What is the formula for surface area? How would you calculate the total surface area for the cube below and the rectangular box below? Follow the procedure for Lesson 7.1 “Increasing the Surface Area of a Clay Cube” on page 51 in your textbook. Answer these questions as you complete the activity. How would you define the surface area of the clay? Calculate the surface area of the cube you made. Show your measurements and calculations. How can you increase the surface area of your cube without greatly increasing the volume it occupies and being able to still calculate the total surface area? You may cut the clay, but all pieces must fit in a box that is slightly larger than the original cube. Explain and draw the idea you and your partner come up with below: Defend your idea that you drew and explained above mathematically. That means calculate the new surface area of your newly designed cube and compare it to the original surface area of the cube you began with. Follow the procedure on page 52 for Inquiry 7.2 “Modeling the Inside Surface of the Small Intestine”. Answer these questions as you complete the inquiry. You are modeling the lining of the small intestine. Assuming that one side of each two-part ticket has a surface area of approximately 25 square centimeters, what would be the total surface area of the inside of the cylinder? Record this value and show your work. Compare your model of the small intestine with the illustration of the small intestine in Figure 7.2 in your textbook. Calculate the surface area of the inside of the folded strip of tickets and record. Compare the surface areas of the folded and unfolded tickets and express the relationship between the surface areas as a ratio. Why might increasing the surface area of food be important to digestion? List some advantages of the enormous surface area of the small intestine: What other human organs might need a large surface area? If so, which ones? Why? Which would dissolve faster in a cup of hot water: a sugar cube or a teaspoon of sugar (assuming equal amounts)? Defend your answer. What might a human look like if he or she had no folds in the small intestine? Why? Many tools and instruments we use in daily life are designed with folds. How many can you think of? What are the advantages of folds? What happens to water and undigested wastes in the large intestine? What happens if food moves too quickly or too slowly through the large intestine? Why do your parents tell you to hang up your wet swimsuit or wet towel instead of leaving it in a ball on the floor? What does this have to do with surface area?
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