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

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

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

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

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

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

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

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

1 1 1 original 1 x2 8 2 2 2

1 1 1 original 1 x2 8 3 x3 27 3 3

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

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 =

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

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

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

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

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

2 3 S P A V r r2 r3 r

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

Scale Factor Side Perimeter Area Surface Area Volume r

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.

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

Not similar

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

2 3 S P A V

2 3 S P A V

2 3 S P A V

2 3 S P A V

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 A 2

S A 2

S A 2

S A 2

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

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. 2 3 S P A V