7th Grade Math

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Similar Solids

PART A B C

Multi-Part

Lesson 2

GLE 0706.4.3

Understand and use scale

factor to describe the

relationships between

length, area, and volume.

SPI 0706.4.3 Apply scale

factor to solve problems

involving area and volume.

Also addresses GLE 0706.1.3.

654 Measurement and Proportional Reasoning

Changes in Dimensions

MODELS Stephen is creating a model of

the Washington Monument for history class.

The model will be _^1

100

of the monument’s

actual size.

1. The pyramid that sits atop the
   monument’s obelisk shape has
   a height of 55.5 feet. What is the
   height of the pyramid on the
   model Stephen is creating?


2. MAKE A CONJECTURE Write a sentence
   about the area of the triangular
   side of the model compared
   with the actual monument.

Cubes are similar solids because they have the same shape and their

corresponding linear measures are proportional.

The cubes at the right are similar.

The ratio of their corresponding

edge lengths is _^8

4

or 2. The scale

factor is 2. How are their surface

areas related?

S.A. of Small Cube S.A. of Large Cube

S.A. = 6(4)(4)

There are 6 faces.

S.A. = 6( 2 · 4)( 2 · 4)

= 2 · 2 (6)(4 · 4)

= 22 (6)(4 · 4)

To find the surface area of the large cube, multiply the surface area

of the small cube by the square of the scale factor, 2^2 or 4. This

relationship is true for any similar solids.

Surface Area of Similar Solids

If Solid X is similar to Solid Y by a scale factor, then the surface

area of X is equal to the surface area of Y times the square of the

scale factor.

theW

Main Idea

Solve problems

involving similar solids.

Vocabulary

similar solids

V

s

4 in. 8 in.

8 in.

8 in.

4 in.

4 in.

652_659_C11_L2_895130.indd 654 12/30/09 4:39 PM