Areas and Volumes of Similar Solids

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Areas and Volumes of Similar Solids

• 10-6

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Definitions

• Similar Solids solids with the same shape and
  all corresponding dimensions are proportional
• Similarity Ratio the ratio of corresponding
  dimensions of two similar solids

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Theorem 10-7 Areas and Volumes of Similar Solids

• If the similarity ratio of two similar solids is
  ab then
• 1) the ratio of their corresponding areas is a2
  b2
• 2) the ratio of their volumes is a3 b3

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The lateral areas of two cylinders are 196?in.2
and 324 ?in.2. The volume of the smaller cylinder
is 686 ?in.3. Find the volume of the larger
cylinder.

• First find the similarity ratio a b
• a2/b2 196 ?/324 ?
• a2/b2 49/81
• a/b 7/9
• V1/V2 73/93
• 686?/V2 343/729
• 343V2 686 ? (729)
• V2 1458 ?
• The volume of the larger cylinder is 1458 ?in3

• The ratio of the S.A. is a2/b2
• Divide the numerator and denominator by 4 ?
• Find the sq. root
• The ratio of volumes is a3/b3
• Sub 686 ? for V1
• Cross Products
• Divide by 343

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A marble paperweight shaped like a pyramid weighs
.15lbs. How much does a similarly shaped
paperweight weigh if each dimension is three
times larger?

• The similarity ratio is 13 so the ratio of
  volumes is 13 33 or 1 27
• 1/27 .15/x
• x 27 (.15)
• x 4.05
• The larger marble weighs about 4 lbs.

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Homework

• P 533 1-17 not 15