12.7 Exploring Similar Solids Hubarth Geometry

Two solids of the same type with equal ratios of corresponding linear measures, such as height or radii, are called similar solids. Ex 1 Identify Similar Solids Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right. a. b. The prisms are similar because the ratios of corresponding linear measures are all equal. The scale factor is 2:3. The prisms are not similar because the ratios of corresponding linear measures are not all equal.

The cans shown are similar with a scale factor of 87:100. Find the surface area and volume of the larger can. Ex 2 Use the Scale Factor of Similar Solids Surface area of I Surface area of II Surface area of II Volume of I Volume of II Volume of II a2a2 b2b2 = = a3a3 b3b3 = = Volume of II ≈ Surface area of II ≈ 68.49

Ex 3 Find the Scale Factor The pyramids are similar. Pyramid P has a volume of 1000 cubic inches and Pyramid Q has a volume of 216 cubic inches. Find the scale factor of Pyramid P to Pyramid Q. a3a3 b3b3 = The scale factor of Pyramid P to Pyramid Q is 5:3. a b = 5 3

A store sells balls of yarn in two different sizes. The diameter of the larger ball is twice the diameter of the smaller ball. If the balls of yarn cost $7.50 and $1.50, respectively, which ball of yarn is the better buy? Volume of large ball Volume of small ball Compute: the ratio of volumes using the diameters = = 8 1, or 8 : 1 Ex 4 Compare Similar Solids Price of large ball Price of small ball Find: the ratio of costs. =, or 5:1 5 1 = $ 1.50 $ 7.50 Compare: the ratios in Steps 1 and 2. If the ratios were the same, neither ball would be a better buy. Comparing the smaller ball to the larger one, the price increase is less than the volume increase. So, you get more yarn for your dollar if you buy the larger ball of yarn. The larger ball of yarn is the better buy.