1. Area and Volume Ratios 8.6

2. Learn the perimeter, area, and volume ratios of similar solids.
Define similar solids.
Learn the perimeter, area, and volume ratios of similar solids.
Use the ratios to find missing measurements.
homework

3. 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.
homework

4. Perimeter and Area Ratios
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5. Surface Area and Volume Ratios
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6. Proportional Angle Bisector Theorem
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7. Proportional Altitudes TheoremB C D
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8. Proportional Medians Theorem
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9. The solid is similar to a larger solid with the given
scale factor. Find the surface area S and volume V of the larger solid.
homework

10. Use the given information about the two similar solids to find their scale factor.
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11. 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.
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.
homework

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

13. ABC Lumber Company sells plans and materials for several storage sheds
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.

14. Softballs and baseballs are both used to play a game with a bat
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.

15. Two sizes of balloons are being used for decorating at a party
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..
18 in.
7 in.
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.
9:7
81:49
729:343

16. 8.6 Area, Length, and Volume Ratios
Assignment
8.6 Area, Length, and Volume Ratios