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8.7

8.7. How Does The Measure Change? pg. 20 Similar Solids. 8.7 – How Does the Measure Change? Similar Solids. As you continue your study of three-dimensional solids, you will explore how the volume of a solid changes as the solid is enlarged proportionally. 8.33 –DIMENSIONS

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8.7

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  1. 8.7 How Does The Measure Change? pg. 20 Similar Solids

  2. 8.7 – How Does the Measure Change? Similar Solids As you continue your study of three-dimensional solids, you will explore how the volume of a solid changes as the solid is enlarged proportionally.

  3. 8.33 –DIMENSIONS What is the difference in dimensions? Examine this idea below. a. What does an object with zero dimensions look like? Draw a picture. What measurements are found in one dimension? What happens when you double it in size? Triple? Quadruple? point nothing A

  4. b. What does an object with one dimensions look like? Draw a picture. What measurements are found in one dimension? What happens when you double it in size? Triple? Quadruple? x2 Segment, perimeter x3 A B x4

  5. c. What does an object with two dimensions look like? Draw a picture. What measurements are found in two dimensions? What happens when you double it in size? Triple? Quadruple? Plane, polygons original 1 D C 1 A B 1

  6. D C 1 A B 1 original 1 D C x2 4 2 A B 2

  7. D C 1 A B 1 original 1 D C x2 4 3 x3 9 A B 3

  8. D C 1 A B 1 original 1 D C x2 4 4 x3 9 A B x4 16 4

  9. d. What does an object with three dimensions look like? Draw a picture. What measurements are found in three dimensions? What happens when you double it in size? Triple? Quadruple? Cubes original 1 1 1 1

  10. 1 1 1 original 1 x2 8 2 2 2

  11. 1 1 1 original 1 x2 8 3 x3 27 3 3

  12. 1 1 1 original 1 x2 8 4 x3 27 4 x4 64 4

  13. 8.34 –RATIO OF SIMILAR FIGURES a. Examine the two prisms. Are the two prisms similar? yes 2 3 4 6 2 3 = 8 12 2 3 =

  14. b. What is the ratio of the edges? 2 3 2 3

  15. c. What is the ratio of the Perimeter of the Bases? 2 3 12 18

  16. d. What is the ratio of the Area of the Base? 4 9 8 18

  17. e. What is the ratio of the surface areas? 4 9 112 252

  18. f. What is the ratios of the volumes? 8 27 64 216

  19. 2 3 S P A V r r2 r3 r

  20. g. What if the ratio was different? Complete the table.

  21. 8.35 –SIMILAR SOLIDS Determine if the figures are similar. If they are find the scale factor of the sides, perimeter, area, surface area, and volume.

  22. 5/2 5/2 similar 5/2 25/4 25/4 125/8

  23. Not similar

  24. 8.36 –RATIO OF SIMILAR FIGURES The following figures are similar. Find the scale factor of the solids.

  25. 2 3 S P A V

  26. 2 3 S P A V

  27. 2 3 S P A V

  28. 2 3 S P A V

  29. 8.37 –RATIO OF SIMILAR FIGURES Corresponding lengths in similar figures are given. Find the ratios (shaded to unshaded) of the perimeters and areas. Find the unknown area.

  30. 2 SA

  31. 2 SA

  32. 2 SA

  33. 2 SA

  34. 8.39 –EXTRA PRACTICE a. A shipping box holds 450 golf balls. A similar larger shipping box has dimensions triple the size of the box. How many golf balls does the larger box hold? 2 3 S P A V 3 27 450 x 27 = 12,150

  35. b. Two containers are similar. The smaller container has a surface area of 36m2 and a volume of 8m3. The larger container has a volume of 27m3. Find the larger container's surface area. 2 3 S P A V

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