Area and Volume Ratios 8.6Area and Volume Ratios 8.6

• Define similar solids.

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• Learn the perimeter, area, and volume ratios of similar solids.

• Use the ratios to find missing measurements.

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Similar solids are solids that have the same shape but are not necessarily the same size. Just as with similar polygons, corresponding linear measures have equivalent ratios.

Perimeter and Area RatiosPerimeter and Area Ratios

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Surface Area and Volume RatiosSurface Area and Volume Ratios

Proportional Angle Bisector Theorem

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A. A

B. B

C. C

D. D

Proportional Altitudes Theorem

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Proportional Medians Theorem

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The solid is similar to a larger solid with the givenscale factor. Find the surface area S and volume V of the larger solid.

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Use the given information about the two similar solids to Use the given information about the two similar solids to find their scale factor.find their scale factor.

The scale factor of the model car at the right to the actual car is 1:16. Use the scale factor to complete the exercises.

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a. The model has a height of 5.5 inches. What is the height of the actual car?

b. Each tire of the model has a surface area of 12.9 square inches. What is the surface area of each tire of the actual car?

c. The model’s engine has a volume of 2 cubic inches. Find the volume of the actual car’s engine.

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You are given two similar solids.You are given two similar solids. Find the missing Find the missing measurement. Then calculate the surface area and volume measurement. Then calculate the surface area and volume of each solid.of each solid.

ABC Lumber Company sells plans and materials for several storage sheds. The two designs shown have a similar shape, but differ in size.

a. Find the scale factor of the shed on the left to the shed on the right.

b. Find the ratios of the surface areas and the volumes.

Softballs and baseballs are both used to play a game with a bat. A softball has a diameter or 3.8 inches, while a baseball has a diameter of about 2.9 inches. Find the scale factor of the two balls.

Write the ratio of the corresponding measures of the balls.

Substitution

Simplify.

Answer: The scale factor is about 1.3:1.

Two sizes of balloons are being used for decorating at a party. When fully inflated, the balloons are spheres. The first balloon has a diameter of 18 inches while the second balloon has a radius of 7 inches..a. Find the scale factor of the two balloons.

b. Find the ratio of the surface areas of the two balloons.

c. Find the ratio of the volumes of the two balloons.

81:49

729:343

9:7

18 in. 7 in.

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8.6 Area, Length, and 8.6 Area, Length, and Volume RatiosVolume Ratios