10-8 Areas and Volumes of Similar Solids

Similar solids have the same shape, and all their corresponding dimensions are proportional.

The ratio of corresponding linear dimensions of two similar solids is the similarity ratio.

Any two cubes are similar. Any two spheres are similar.

Are the two solids similar?

Are the two solids similar?

Are the two solids similar?

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.

The two solids are similar. Find the similarity ratio, the ratio of the areas, and the ratio of the volumes.

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

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

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

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

Homework:

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