Volume%20ratios%20of%20similar%20solids

1
Volume ratios of similar solids
2
Theorem 99-1

• If 2 similar solids have a scale factor of ab,
  then,
• 1. the ratio of the perimeters of their
  corresponding faces is ab
• 2. the ratio of the areas of their corresponding
  faces is a2b2
• 3. the ratio of their volumes is a3b3

3
Corrsponding perimeters of similar solids

• The scale factor is 32, find the perimeter of
  the smaller pyramid's base.
• P337.57.5 21
• 21 3
• P 2
• 3P 42
• P 14

7.5 in.
3 in.
4
Find perimeter of similar solid

• Find perimeter of the larger square pyramid, if
  the scale factor is 43

7.5 cm.
5
Findins surface ares of similar solids

• The surface area of the larger pyramid is 392
  square cm., What is the surface area of the
  smaller pyramid.
• 142 392
• 102 S

14 cm.
10 cm
6
Finding surface areas of similar solids

• Find the surface area of the smaller triangular
  prism, if the surface area of the larger is 325

7
Finding volumes of similar solids

• The 2 cylinders are similar. If the volume of the
  smaller is 38 cubic feet, what is the volume of
  the larger cylinder?
• 33 V
• 23 38

R 3 ft
R 2 ft
8
Finding volumes of similar prisms

• 2 similar prisms are shown. The volume of the
  larger prism is 364.8 cubic cm., what is the
  volume of the smaller to the nearest tenth?

16 cm.
9 cm.
9
practice

• 2 similar triangular prisms have a scale factor
  of 34
• A) find perimeter
• of the larger's base
• B) If surface area of
• smaller is 182 sq. in.,
• find the surface area of larger
• C) If volume of smaller is 323 cu. In., find
  volume of larger

15 in.
8 in.
17 in.