1. How Does The Measure Change? pg. 20 Similar Solids
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. point nothing A 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. x2 Segment, perimeter x3 A B x4
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. Plane, polygons original 1 D C 1 A B 1
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
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. yes 2 3 4 2 6 3 8 2 12 3 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.
S P A V r r2 r3 r

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

21. Scale Factor
Side
Perimeter
Area
Surface Area
Volume r

22. 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.

23. 5/2
5/2
similar
5/2
25/4
25/4
125/8

24. Not similar

25. 8.36 –RATIO OF SIMILAR FIGURES
The following figures are similar. Find the scale factor of the solids.

26.
S P A V

27.
S P A V

28.
S P A V

29.
S P A V

30. 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.

31. S A 2

32. S A 2

34. S A 2

35. S A 2

36. 2 3 S P A V 3 27 450 x 27 = 12,150 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?
S P A V 3 27
450
x 27 =
12,150

37. b. Two containers are similar
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.
S P A V