8.7

How Does The Measure Change?

pg. 20Similar 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 –DIMENSIONSWhat 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?

Apoint nothing

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?

Segment, perimeter x2

A B

x3

x4

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

A B

CD

1

1

1original

A B

CD

1

1

A B

CD

2

2

1original

4x2

A B

CD

1

1

A B

CD

3

3

1original

4x2

9x3

A B

CD

1

1

A B

CD

4

4

1original

4x2

9x3

16x4

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

1original

1

1

1

1original1

1

1

2

2

2

8x2

1original1

1

1

3

3

3

8x2

27x3

1original1

1

1

4

4

4

8x2

27x3

64x4

8.34 –RATIO OF SIMILAR FIGURESa. Examine the two prisms. Are the two prisms similar?

23

46

=23

812

=23

yes

b. What is the ratio of the edges?

2 323

c. What is the ratio of the Perimeter of the Bases?

12 1823

d. What is the ratio of the Area of the Base?

8 1849

e. What is the ratio of the surface areas?

112 25249

2 8 12 8SA 2 18 18 12SA

f. What is the ratios of the volumes?

64 216 827

8 8V 18 12V

S P A V

r r r2 r3

2 3

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

Scale Factor

Side Perimeter AreaSurface

AreaVolume

r

6

1

4

75

9

6

1

6

1

36

1

36

1

216

1

4

7

4

7

16

49

16

49

64

3435

9

5

9

25

81

25

81

125

729

r r 2r 2r 3r

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

similar

5/2

5/2

5/2

25/425/4

125/8

Not similar

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

36

121

6

11

S P A V

36

121

2 3

6

11

216

1331

150

2945

7

S P A V25

49

2 3

5

7

125

343

125

216

5

6

S P A V2 3

5

6

25

36

64

125

S P A V64

1254

5

2 3

4

5

16

25

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.

S A1

162

8

2

1

4 3

x

x 48 ft 2

S A9

259

15

2

3

5

225

x

25x 2025281x in

S A144

3612

6

2

12x 605x in

10

x

S A168

378

2

3

2

2x 2412x cm

8

x

4

9

8.39 –EXTRA PRACTICEa. 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

2 3

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

34

9

S P A V

4

9

8

27

36

x281x m

2 3