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

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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.

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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? A pointnothing

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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

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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

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AB C D 1 1 AB C D 2 2 1 4x2

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

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AB C D 1 1 AB C D 4 4 1original 4x2 9x3 16x4

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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

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1 1 1 1 2 2 2 8x2

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

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

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8.34 –RATIO OF SIMILAR FIGURES a. Examine the two prisms. Are the two prisms similar? 2323 4646 = 2323 8 12 = 2323 yes

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b. What is the ratio of the edges? 23 2323

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c. What is the ratio of the Perimeter of the Bases? 1218 2323

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d. What is the ratio of the Area of the Base? 818 4949

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e. What is the ratio of the surface areas? 112252 4949

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f. What is the ratios of the volumes? 64216 8 27

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SPAVSPAV r r r2r2 r3r3 2 3

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

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Scale Factor SidePerimeterArea Surface Area Volume r

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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.

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similar 5/2 25/4 125/8

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Not similar

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

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SP A V 2 3

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SPAVSPAV

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SPAVSPAV

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SPAVSPAV

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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.

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SASA 2

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SASA 2

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SASA 2

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SASA 2

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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? SPAVSPAV 327 450x 27 = 12,150 2 3

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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

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