10-8 Areas and Volumes of Similar Solids

1
10-8 Areas and Volumes of Similar Solids
2
Similar solids have the same shape, and all their
corresponding dimensions are proportional.
3
The ratio of corresponding linear dimensions of
two similar solids is the similarity ratio. Any
two cubes are similar. Any two spheres are
similar.
4
Are the two solids similar?
5
Are the two solids similar?
6
Are the two solids similar?
7
Areas and Volumes of Similar Solids If the
similarity ratio of two similar solids is a b,
then 1. The ratio of their corresponding areas
is a2 b2. 2. The ratio of their volumes is a3
b3.
8
The two solids are similar. Find the similarity
ratio, the ratio of the areas, and the ratio of
the volumes.
9
The surface areas of two similar figures are
given. The volume of the larger figure is given.
Find the volume of the smaller figure.
S.A. 25 cm2 S.A. 36 cm2 V 216 cm3
10
The surface areas of two similar figures are
given. The volume of the larger figure is given.
Find the volume of the smaller figure.
S.A. 16 in2 S.A. 25 in.2 V 500 in.3
11
The volumes of two similar figures are given. The
surface area of the smaller figure is given. Find
the surface area of the larger figure.
V 8 ft3 V 125 ft3 S.A. 4 ft2
12
The volumes of two similar figures are given. The
surface area of the smaller figure is given. Find
the surface area of the larger figure.
V 40 m3 V 135 m3 S.A. 40 m2
13
Homework p. 5681 - 16