Lesson 13-4

Example 1  Similar and Congruent Solids
Determine whether each pair of solids are similar, congruent, or neither.
a.	Find the ratios between the corresponding parts of the square pyramids.
			= 	Substitution
		= 	Simplify.
		= 	Substitution
		= 	Simplify.	

	The ratios of the measures are equal, so we can conclude that the pyramids are similar. Since the scale factor is not 1, the solids are not congruent.

b.	Compare the ratios between the corresponding parts of the cylinders.
			= 	Substitution
		= 2	Simplify.
		= 	Substitution
		= 	Simplify.	

	The ratio of the radii of the cylinders does not equal the ratio of the heights of the cylinders. The cylinders are not similar and not congruent.

Example 2  Spheres
SPORTS  The balls used in golf and tennis are spheres that are required to have standard measurements. A golf ball is not to be less than 1.68 inches in diameter. A tennis ball is not to exceed 2 inches in diameter. Consider a golf ball with a diameter of 1.68 inches and a tennis ball with a diameter of 2 inches.
a.	Find the scale factor of the two spheres.
	Write the ratio of the corresponding measures of the spheres.
		= 	Substitution
		=  or 	Simplify.

	The scale factor is 16 : 25.

b.	Find the ratio of the surface areas of the two balls.
	If the scale factor is a : b, then the ratio of the surface areas is a2 : b2.
		= 	Theorem 13.1
		= 	a = 16, b = 25
		= 	Simplify.
	The ratio of the surface area is 256 : 625.

c.	Find the ratio of the volumes of the two spheres.
	If the scale factor is a : b, then the ratio of the volumes is a3 : b3.
		= 	Theorem 13.1
		= 	a = 16, b = 25
		= 	Simplify.
The ratio of the volumes is 4096 : 15,625.