12.7 Similar Solids Geometry

Objectives Find and use the scale factor of similar solids. Use similar solids to solve real-life problems.

Comparing Similar Solids Two solids with equal ratios of corresponding __________measure s, such as heights or radii, are called similar solids. This common ratio is called the _________ of one solid to the other solid.

Comparing Similar Solids Any two _______ are similar; so are any two __________. Here are other examples of similar and nonsimilar solids.

Ex. 1: Identifying Similar Solids Decide whether the two solids are similar. If so, compare the surface areas and volumes of the solids.

Solution:

More... The surface area and volume of the solids areas follows: PrismSurface AreaVolume Smaller S = 2B + Ph=V = Bh = Larger S = 2B + Ph=V = Bh = The ratio of side lengths is 1:2, the ratio of the surface areas is ______, or ____, and the ratio of the volumes is ______, or ____.

Theorem: Similar Solids If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of ______, and corresponding volumes have a ratio of ______. The term areas in the theorem can refer to any pair of corresponding areas in the similar solids, such as lateral areas, base areas, and surface areas.

Ex. 2: Using the scale factor of similar solids The prisms are similar with a scale factor of 1:3. Find the surface area and volume of prism G given that the surface area of prism F is 24 square feet and the volume of prism F is 7 cubic feet.

Solution: Begin by using Theorem to set up the two proportions.

Check your work You can check your work by substituting back into original proportions.

Ex. 3: Finding the scale factor of similar solids To find the scale factor of the two cubes, find the ratio of the two volumes.

Ex. 5: Comparing Similar Solids Swimming pools. Two swimming pools are similar with a scale factor of 3:4. The amount of chlorine mixture to be added is proportional to the volume of water in the pool. If two cups of chlorine mixture are needed for the smaller pool, how much of the chlorine mixture is needed for the larger pool?

Solution: Using the scale factor, the ratio of the volume of the smaller pool to the volume of the larger pool is as follows:

Assignment: Pg 769 #