7th Grade Math

Lesson 2B Similar Solids 653

Changing dimensions of a three-dimensional figure also affects the surface

area and volume.

Find the volume and surface area of one

1 cm

1 cm

centimeter cube. Then record the data in 1 cm

a table like the one below.

Create a cube with side lengths that

2 cm

2 cm

2 cm

are double that of the previous cube.

Find the volume and surface area and

record the data in the table.

Triple the side lengths of the original

centimeter cube. Find the volume and

surface area and record the data in the table.

For each cube, Side

Length

(units)

Volume

(units^3 )

Surface Area

(units^2 )

Ratio of

Side Length

to Volume

Ratio of Side

Length to

Surface Area

113 = 1 6 (1^2 ) 1 : 1 1 : 6

2

3

4

s

write a ratio

comparing the

side length and

the volume.

Then write a

ratio comparing

the side length

and the surface

area. The first one

is done for you.

and Apply

3. MAKE A CONJECTURE How does doubling the dimensions of a three-
   dimensional figure affect the volume of the figure? surface area?


4. PIZZA A pizza restaurant advertised the

PIZZA

by

0AT

5

$ 399

10

15

personal pizza

medium pizza $ 999

family size $ 1499

special at the right. The dimensions

given are the diameters of each pizza.

a. What is the area of each pizza?

Use A = 3.14r^2.

b. What is the ratio of the area of the personal

pizza and the medium pizza?

c. How does the area of a circle change when

the diameter is doubled? tripled?

652_659_C11_L2_895130.indd 653 12/30/09 4:39 PM