Transcript Areas and Volumes of Similar Solids LESSON 11-7 Additional Examples Are the two solids similar? If so, give the similarity ratio. Both solid figures.

Areas and Volumes of Similar Solids
LESSON 11-7
Additional Examples
Are the two solids similar? If so, give the similarity ratio.
Both solid figures have the same shape. Check that the ratios of the
corresponding dimensions are equal.
8
The ratio of the radii is 3 , and the ratio of the height is 26 .
9
The cones are not similar because 3 =/ 8 .
26
9
Quick Check
HELP
GEOMETRY
Areas and Volumes of Similar Solids
LESSON 11-7
Additional Examples
Find the similarity ratio of two similar cylinders with surface
areas of 98 ft2 and 2 ft2.
Use the ratio of the surface areas to find the similarity ratio.
a2 98
=
b2
2
The ratio of the surface areas is a2 : b2.
a2 49
=
b2
1
Simplify.
a
7
=
b
1
Take the square root of each side.
The similarity ratio is 7 : 1.
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HELP
GEOMETRY
Areas and Volumes of Similar Solids
LESSON 11-7
Additional Examples
Two similar square pyramids have volumes of 48 cm3 and 162
cm3. The surface area of the larger pyramid is 135 cm2. Find the
surface area of the smaller pyramid.
Step 1: Use the ratio of the volumes to find the similarity ratio.
a3
48
=
3
b
162
The ratio of the volumes is a3 : b3.
8
a3
=
27
b3
Simplify.
a
2
=
b
3
Take the cube root of each side.
HELP
GEOMETRY
Areas and Volumes of Similar Solids
LESSON 11-7
Additional Examples
(continued)
Step 2: Use the similarity ratio to find the surface area S1 of the smaller
pyramid.
S1 22
= 2
The ratio of the surface areas is a2 : b2.
S2 3
S1 4
=
Simplify.
S2 9
S1 4
=
Substitute 135 for S2, the surface area of the larger
135 9
pyramid.
S1 = 4 • 135
9
Solve for S1.
S1 = 60
Simplify.
The surface area of the smaller pyramid is 60 cm2.
HELP
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GEOMETRY
Areas and Volumes of Similar Solids
LESSON 11-7
Additional Examples
A box of detergent shaped like a rectangular prism is 6 in.
high and holds 3.25 lb of detergent. How much detergent would a
similar box that is 8 in. tall hold? Round your answer to the nearest
tenth.
The ratio of the heights of the boxes is 6 : 8, so the similarity ratio is 6 : 8,
or 3 : 4 in simplest terms.
Because the weights are proportional to the volumes, the ratio of the
weights equals the cube of their similarity ratio: 33 : 43, or 27 : 64.
HELP
GEOMETRY
Areas and Volumes of Similar Solids
LESSON 11-7
Additional Examples
(continued)
27 3.25
=
64
x
Let x  the weight of the larger box of detergent.
27x = 64  3.25
Cross-Product Property.
27x = 208
Simplify.
x
7.7037037
Divide each side by 27.
The box that is 8 in. tall would hold about 7.7 lb of detergent.
Quick Check
HELP
GEOMETRY