7.7 How Does The Measure Change? pg. 19 Similar Solids.

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Presentation transcript:

7.7 How Does The Measure Change? pg. 19 Similar Solids

7.7 – 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.

7.33 –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? A pointnothing

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 AB 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 AB C D 1 1 1original

AB C D 1 1 AB C D x2

AB C D 1 1 AB C D 3 3 1original 4x2 9x3

AB C D 1 1 AB C D 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

x2

1original x2 27x3

1original x2 27x3 64x4

7.34 –RATIO OF SIMILAR FIGURES a. Examine the two prisms. Are the two prisms similar? = = 2323 yes

b. What is the ratio of the edges?

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

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

e. What is the ratio of the surface areas?

f. What is the ratios of the volumes?

SPAVSPAV r r r2r2 r3r3 2 3

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

Scale Factor SidePerimeterArea Surface Area Volume r

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

similar 5/2 25/4 125/8

Not similar

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

SPAVSPAV 2 3

SPAVSPAV

SPAVSPAV

SPAVSPAV

7.37 –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? SPAVSPAV x 3 3 = 12,

b. Two containers are similar. The smaller container has a surface area of 36m 2 and a volume of 8m 3. The larger container has a volume of 27m 3. Find the larger container's surface area. SPAVSPAV 2 3