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. 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

7. 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