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 the Similar Solids Theorem to write and solve two proportions.
Surface area of I
Surface area of II a2 b2 =
Volume of I
Volume of II = a3 b3
51.84
Surface area of II =
872
1002
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 the Similar Solids Theorem to find the ratio of the two volumes.
EXAMPLE 3
Find the scale factor
SOLUTION
Use the Similar Solids 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. 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.
Scale factor is 3 : 5;
Volume of D =
125 square units
Edge length is 3 units;
ANSWER

10. Daily Homework Quiz
for Examples 2, 3, and 4
Two triangular prisms are similar, with surface areas 9 ft2 and 25 ft2 . What is the scale factor of the prisms? 1.
ANSWER
3 : 5
Two spheres have volumes 125π m3 and 216π m3. What is the scale factor of the spheres? What is the ratio of the surface areas? 2.
ANSWER
5 : 6; 25 : 36

11. Daily Homework Quiz
The volumes of two similar square pyramids are 8 ft3 and 27 ft3. What is the ratio of the surface area of the smaller pyramid to the larger? 3.
ANSWER
4 : 9
The two solids are similar. Find the surface area and volume of Solid II. 4.
ANSWER
S = cm2; V = cm3