9-5

1. 9-5 Changing Dimensions Course 2 Warm Up Problem of the Day Lesson Presentation

2. 9-5 Changing Dimensions Course 2 Warm Up Find the surface area of each figure to the nearest tenth. Use 3.14 for . 1.a cylinder with radius 5 ft and height 11 ft 2. a sphere with diameter 6 ft 3. a rectangular prism 9 ft by 14 ft by 6 ft 502.4 ft2 113.0 ft2 528 ft2

3. 9-5 Changing Dimensions Course 2 Problem of the Day If 6 cats can catch 6 mice in 6 minutes, how many cats are needed to catch 10 mice in 10 minutes? 6 cats

4. 9-5 Changing Dimensions Course 2 Learn to find the volume and surface area of similar three-dimensional figures.

5. 9-5 Changing Dimensions Course 2 Recall that similar figures are proportional. The surface areas of similar three-dimensional figures are also proportional. To see this relationship, you can compare the areas of corresponding faces of similar rectangular prisms.

6. 9-5 Changing Dimensions Remember! You can multiply the numbers in any order. So (3 · 2) · (5 · 2) is the same as (3 · 5) · (2 · 2). Course 2 Area of front of smaller prism Area of front of larger prism 6 · 10 3 · 5 (3 · 2) · (5 · 2) 15 Each dimension has a scale factor of 2. (3 · 5) · (2 · 2) 15· 22

7. 9-5 Changing Dimensions Course 2 The area of the front face of the larger prism is 22 times the area of the front face of the smaller prism. This is true for all of the corresponding faces. Thus it is also true for the entire surface area of the prisms. surface area of figure A surface area of figure B (scale factor of figure A)2 = •

8. 9-5 Changing Dimensions Course 2 Additional Example 1A: Finding the Surface Area of a Similar Figure The surface area of a box is 35 in2. What is the surface area of a larger, similarly shaped box that has a scale factor of 7? Use the surface area of the smaller box and the square of the scale factor. S = 35 · 72 S = 35 · 49 Evaluate the power. Multiply. S = 1,715 The surface area of the larger box is 1,715 in2.

9. 9-5 Changing Dimensions Course 2 Additional Example 1B: Finding the Surface Area of a Similar Figure The surface area of a box is 1,300 in2. Find the surface area of a smaller, similarly shaped box that has a scale factor of 1 2 . Use the surface area of the original box and the square of the scale factor. 2 1 2 S = 1,300 · 1 4 S = 1,300 · Evaluate the power. S = 325 Multiply. The surface area of the smaller box is 325 in2.

10. 9-5 Changing Dimensions Course 2 Insert Lesson Title Here Try This: Example 1A The surface area of a box is 50 in2. What is the surface area of a larger, similarly shaped box that has a scale factor of 3? Use the surface area of the smaller box and the square of the scale factor. S = 50 · 32 Evaluate the power. S =50 · 9 Multiply. S = 450 The surface area of the larger box is 450 in2.

11. 9-5 Changing Dimensions Course 2 Try This: Example 1B The surface area of a box is 1,800 in2. Find the surface area of a smaller, similarly shaped box that has a scale factor of 1 3 . Use the surface area of the original box and the square of the scale factor. 2 1 3 S = 1,800 · 1 9 S = 1,800 · Evaluate the power. S = 200 Multiply. The surface area of the smaller box is 200 in2.

12. 9-5 Changing Dimensions Course 2 The volumes of similar three-dimensional figures are also related. 2 ft 4 ft 1 ft 2 ft 3 ft 6 ft Volume of smaller box Volume of larger box 2 · 3 · 1 4 · 6 · 2 (2 · 2) · (3 · 2) · (1 · 2) 6 (2 · 3 · 1) · (2 · 2 · 2) The volume of the larger box is 23 times the volume of the smaller box. 6· 23 Each dimension has a scale factor of 2.

13. 9-5 Changing Dimensions Course 2 volume of figure B (scale factor of figure A)3 volume of figure A • =

14. 9-5 Changing Dimensions Course 2 Additional Example 2: Finding Volume Using Similar Figures The volume of a prism is 28 ft3. What is the volume of a larger, similar shaped prism that has a scale factor of 4? Use the volume of the smaller prism and the cube of the scale factor. V = 28 · 43 Evaluate the power. V = 28 · 64 V = 1,792 Multiply. The volume of the larger prism is 1,792 ft3.

15. 9-5 Changing Dimensions Course 2 Insert Lesson Title Here Try This: Example 2 The volume of a prism is 48 ft3. What is the volume of a larger, similar shaped prism that has a scale factor of 2? Use the volume of the smaller prism and the cube of the scale factor. V = 48 · 23 Evaluate the power. V = 48 · 8 V = 384 Multiply. The volume of the larger prism is 384 ft3.

16. 9-5 Changing Dimensions Course 2 When similar three-dimensional figures are made of the same material, their weights compare in the same way as their volumes. The weight of a three-dimensional figure is the weight of a similar three-dimensional figure multiplied by the cube of the scale factor of the original figure.

17. 9-5 Changing Dimensions 1 Understand the Problem Course 2 Additional Example 3: Problem Solving Application Kevin’s water tank weighs 80 lbs when full. He bought a larger tank with a similar shape that has a scale factor of 3. How much does the new tank weigh when full? The answer will be the weight of the new tank when full. You can find the weight of the larger tank by using the weight of the smaller tank. List the important information: • The smaller tank weighs 80 lbs when full. •The scale factor of the larger tank is 3.

18. 9-5 Changing Dimensions Make a Plan 2 Course 2 Additional Example 3 Continued You can write an equation that relates the smaller tank to the weight of the larger tank. greater weight = lesser weight · (a scale factor)3

19. 9-5 Changing Dimensions 3 Solve Course 2 Additional Example 3 Continued greater weight = lesser weight · (a scale factor)3 = 80 · 33 Substitute. = 80 · 27 Evaluate the power. = 2,160 Multiply. The larger tank weighs 2,160 pounds when full.

20. 9-5 Changing Dimensions 4 Course 2 Additional Example 3 Continued Look Back By estimation, the smaller tank weighs less than 100 pounds when full and 100 · 27 = 2,700 pounds. The answer is reasonable.

21. 9-5 Changing Dimensions 1 Understand the Problem Course 2 Insert Lesson Title Here Try This: Example 3 Helen’s candy jar weighs 1.5 lbs when full of jelly beans. She bought a larger jar with a similar shape that has a scale factor of 2. How much does the new jar weigh when full of jelly beans? The answer will be the weight of the new jar when full. You can find the weight of the larger jar by using the weight of the smaller jar. List the important information: • The smaller jar weighs 1.5 lbs when full. •The scale factor of the larger jar is 2.

22. 9-5 Changing dimensions Make a Plan 2 Course 2 Insert Lesson Title Here Try This: Example 3 Continued You can write an equation that relates weight of the smaller jar to the weight of the larger jar. greater weight = lesser weight · (a scale factor)3

23. 9-5 Changing dimensions 3 Solve Course 2 Insert Lesson Title Here Try This: Example 3 Continued greater weight = lesser weight · (a scale factor)3. = 1.5 · 23 Substitute = 1.5 · 8 Evaluate the power. = 12 Multiply. The larger jar weighs 12 pounds when full.

24. 9-5 Changing Dimensions 4 Course 2 Insert Lesson Title Here Try This: Example 3 Continued Look Back By estimation, the smaller jar weighs less than 2 pounds when full and 2 · 8 = 16 pounds. The answer is reasonable.

25. 9-5 Changing Dimensions Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 Given the scale factor, find the surface area of the similar prism. 1. The scale factor of the larger of two similar triangular prisms is 8. The surface area of the smaller prism is 18 ft2. 2. The scale factor of the smaller of two similar triangular prisms is . 1,152 ft2 1 3 The surface area of the larger prism is 630 ft2. 70 ft2

26. 9-5 Changing Dimensions Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 Given the scale factor, find the volume of the larger prism. 3. The scale factor of the larger of two similar rectangular prisms is 3. The volume of the smaller prism is 12 cm3. 4. The scale factor of the smaller of two similar triangular prisms is 324 cm3 1 2 . The volume of the larger prism is 120 m3. 15 m3