Page 63 - Math Course 3 (Book 2)

Similar Solids

Mo. 8

Lesson 6

Let’s Begin

KEY CONCEPTS:

1. Identify similar solids. Identify Similar Solids
2. Solve problems involving similar solids.
Example

MO. 8 - L6a
Determine whether the pair of solids is similar.

Identifying Similar Solids 12 m 7.5 m

6 m 4 m
Vocabulary A-Z

Let us learn some vocabulary 12 6 Write a proportion comparing
7.5 ≟ 4 radii and heights.
similar solids 12(4) ≟ (7.5)(6) Find the cross products.
Similar solids have the same shape and their
corresponding linear measures are proportional. 48 ≠ 45 Simplify.

The radii and heights are not
Answer proportional so the cylinders are
not similar.
6 cm 2 cm
6 cm 2 cm 2 cm
6 cm
Determine whether the pair of solids is similar.

Key Concept

54 in.
9 in.
Ratio of Similar Solids
9 in. 1.5 in.
Words If two solids are similar with a scale 9 in. 1.5 in.
a
factor of , then the surface areas
b 54 9 Write a proportion comparing
a
have a ratio of ( )² and the volumes 9 ≟ 1.5 corresponding edge lengths.
b
a
have a ratio of ( )³. 54(1.5) ≟ 9(9) Find the cross products.
b
Symbols surface area of Solid A a 81 ≠ 81 Simplify.
surface area of Solid B = ( )²
b
volume of Solid A a
volume of Solid B = ( )³ Answer The corresponding measures are
b
proportional, so the pyramids are
Models similar
a b

solid a solid b
55