anonymous
  • anonymous
Th scale factor of two similar cylinders is 3:4. What is the ratios of the areas in simplest form?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Hero
  • Hero
If the scale factor of two similar solids is a:b, then the ratio of their areas is a^2: b^2 In this case the scale factor of these are 3:4. Therefore the ratio of areas are 3^2: 4^2
Hero
  • Hero
Therefore, if the scale factor of two similar cylinders is 3:4, then the ratio of their areas is 9:16
anonymous
  • anonymous
9:16

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anonymous
  • anonymous
\[ 2\pi (3r)^2 + 2\pi (3r) (3h) : 2\pi (4r)^2 + 2\pi (4r) (4h)\] \[ 9 r^2 + 9rh : 16r^2 + 16rh\] \[ 9 (r^2 + rh) : 16(r^2 + rh)\] \[ 9 : 16\]
Hero
  • Hero
Interesting approach
Hero
  • Hero
Can you create a general formula for that approach?
anonymous
  • anonymous
the general formula is dependant on the formula of the shape your dealing with for cylinder: A=2πr 2 +2πrh Sub each scale factor ratio into the equation (ie r -> (3r), h->(3h)), set as a ratio and reduce where you can. cylinder worked out nice. Is that kinda what you were after>

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