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Converting Fresh Grapes to Dried Grapes: A Study on Water Content

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This lesson explores the conversion of fresh grapes to dried grapes based on their water content. Fresh grapes are composed of 80% water by weight, while dried grapes contain only 15% water. Using these values, students will learn how to calculate how many pounds of dried grapes can be obtained from 34 pounds of fresh grapes. The session also revisits the area of similar figures, using proportions to relate areas of polygons. The significance of understanding similarity in geometry will be emphasized through examples and hands-on problem-solving.

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Converting Fresh Grapes to Dried Grapes: A Study on Water Content

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  1. Clickers Bellwork Fresh grapes contain 80% water by weight, whereas dried grapes contain 15% water by weight. How many pounds of dried grapes can be obtained from 34 pounds of fresh grapes? 14

  2. Bellwork Solution Fresh grapes contain 80% water by weight, whereas dried grapes contain 15% water by weight. How many pounds of dried grapes can be obtained from 34 pounds of fresh grapes? 14

  3. Perimeter and Area of Similar Figures Section 11.3

  4. The Concept • Thus far in this chapter we’ve discussed how to find the area of various figures • Today we’re going to revisit a topic from chapter 6, similarity, and see it’s implications on the topic of area

  5. If we remember from chapter 6, the concept of similarity allows us to use a proportion to solve for unknown sides, as long as the two objects are similar Similarity 15 15 x 20 16 Do we remember if this works with perimeter 10’

  6. We have a way to find the areas of similar polygons as well Theorem 11.7 If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a2:b2 Similarity of Area How does this work? Choose a polygon that we have a formula for the area for and let’s look at Problem #30 on page 742

  7. Find the area of the second triangle Obj 1 Example 8 10 Obj 2 6

  8. Find the Area of Object 2 Obj 1 On your own 6 14 Obj 2 6

  9. Find the Area of Object 2 On your own Obj 1 12 16 Obj 2 18

  10. Solve for x Area=100 On your own 12 Area=60 x

  11. Solve for x Area=55 On your own 12 Area=31 x

  12. You are in the process of buying tablecloths for two circular tables. One table has a radius of 2 feet and an area of 12.57 ft2. The other has a radius 5 feet. How big is the area of the top of the table? On your own

  13. A regular pentagon has a side length of 12 cm and an area of about 248 square centimeters. Another regular pentagon has a perimeter of 140. Find it’s area. On your own

  14. How to figure area in similar figures Most Important Points

  15. Homework 11.3 Exercises 1-4, 9-39 multiples 3

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