1. EXAMPLE 2
Use the scale factor of similar solids
Packaging
The cans shown are similar with a scale factor of 87:100. Find the surface area and volume of the larger can.

2. EXAMPLE 2
Use the scale factor of similar solids
SOLUTION
Use Theorem to write and solve two proportions.
Surface area of I
Surface area of II a2 b2 =
51.84
Surface area of II =
872
1002
Volume of I
Volume of II = a3 b3
28.27
Volume of II =
873
1003

3. EXAMPLE 2
Use the scale factor of similar solids
Surface area of II ≈ 68.49
Volume of II ≈ 42.93
The surface area of the larger can is about square inches, and the volume of the larger can is about cubic inches.
ANSWER

4. EXAMPLE 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.

5. Use Theorem 12.13 to find the ratio of the two volumes.
EXAMPLE 3
Find the scale factor
SOLUTION
Use Theorem to find the ratio of the two volumes. a3 b3 =
1000
216
Write ratio of volumes. a b = 6 10
Find cube roots. a b = 5 3
Simplify.
The scale factor of Pyramid P to Pyramid Q is 5:3.
ANSWER

6. EXAMPLE 4
Checking Solutions of a Linear Inequality
Consumer Economics
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?
STEP 1
Compute: the ratio of volumes using the diameters.
Volume of large ball
Volume of small ball 23 13 = = 8 1
, or 8 : 1

7. EXAMPLE 4
Checking Solutions of a Linear Inequality
STEP 2
Find: the ratio of costs.
Price of large ball
Volume of small ball =
$ 1.50
$ 7.50
= , or 5:1 5 1

8. EXAMPLE 4
Checking Solutions of a Linear Inequality
STEP 3
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.
ANSWER
The larger ball of yarn is the better buy.

9. Use Theorem 12.13 to find the ratio of the two properties.
GUIDED PRACTICE
for Examples 2, 3, and 4
Cube C has a surface area of 54 square units and Cube D has a surface area of 150 square units. Find the scale factor of C to D. Find the edge length of C, and use the scale factor to find the volume of D. 3.
Use Theorem to find the ratio of the two properties.
SOLUTION a2 b2 = 54
150
Write ratio of volumes. a b = 5 3
Find square roots. a b = 3 5
Simplify.

10. Surface area = 54 square units
GUIDED PRACTICE
for Examples 2, 3, and 4
Find the edge length.
Surface area = 54 square units
Single side = 9 units
Edge length = 3 units
Find volume of D
C edge
D edge = 3 5
Use Scale Factor.
D edge = 5
Volume of D =
125 square units

11. GUIDED PRACTICE
for Examples 2, 3, and 4
WHAT IF? In Example 4, calculate a new price for the larger ball of yarn so that neither ball would be a better buy than the other. 4.
SOLUTION
Find the value of the volume ratio of large ball and price of small ball
Volume ratio of large ball
price of small ball
= 12.00
ANSWER
$12.00