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...
Areas & Volumes of Similar Solids Objective: Find relationships between the ratios of the areas and volumes of solids.
Vocabulary the same shape and all their corresponding parts are proportional. Similar solids have ________________________________________________________________ the ratio of their corresponding linear dimensions. The similarity ratio of two solids is ____________________________________________
a2 a3
b3
b2
DNG page 224
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Areas & Volumes of Similar Solids Objective: Find relationships between the ratios of the areas and volumes of solids.
Are the two solids similar? If so, give the similarity ratio?
3 1 9 3
not similar
8 4 26 13 1 4 3 13
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Areas & Volumes of Similar Solids
Objective: Find relationships between the ratios of the areas and volumes of solids. DNG page 225
Find the similarity ratio of two similar cylinders with surface areas of 98 ft2 and 2 ft2 ?
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Areas & Volumes of Similar Solids Objective: Find relationships between the ratios of the areas and volumes of solids. DNG page 224
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 Find the similarity ratio.
Step 2 Use the similarity ratio to find the surface area S1 of the smaller pyramid.
The surface area of the smaller pyramid is 60 cm2.
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Areas & Volumes of Similar Solids Objective: Find relationships between the ratios of the areas and volumes of solids. DNG page 226
1. Are the two cylinders similar? If so, give the similarity ratio.
𝒓𝟏 𝒓𝟐 𝟔 𝟓 𝟔 𝟓
=
𝒉𝟏 𝒉𝟐
≟
𝟏𝟐 𝟏𝟎
=
𝟔 𝟓
𝟔 Yes, similarity ratio is . 𝟓
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Areas & Volumes of Similar Solids Objective: Find relationships between the ratios of the areas and volumes of solids. DNG page 226
2. Find the similarity ratio of two similar prisms with surface areas 144 m2 and 324 m2. 𝑎 = 𝑏
144 324
=
𝟐 𝟑
Yes, similarity ratio is
𝟐 . 𝟑
3. The volumes of two similar solids are 128 m3 and 250 m3.The surface area of the larger solid is 250 m2. What is the surface area of the smaller solid?
