text: My Math Forum Geometric ratios
  
   Algebra Pre-Algebra and Basic Algebra Math Forum
  
   August 10th, 2009, 03:12 PM #1 Newbie   Joined: Aug 2009 Posts: 1 Thanks: 0 Geometric ratios How do I answer these questions? I would like the answer to so I can check the work but I need to know the steps please. 1. The volumes of two similar figures are 729 mm cubed and 2744 mm cubed. If the surface area of the larger figure is 393 mm squared what is the surface area of the smaller figure? 2. The surface area of two figures are 16 in squared and 25 inches squared. If the volume of he larger figure is 500 in cubed, what is the volume of the smaller figure? Answer must be in squared.
   August 10th, 2009, 03:44 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 1. We can determine the surface area of such figure from using the formula of $(\frac{V_1}{V_2})^{\frac{1}{3}}=(\frac{A_1}{A_2})^ {\frac{1}{2}}$, where letting an such object having volume of $V_1$ and surface area of $A_1$, and the other object having volume of $V_2$ and surface area of $A_2$. Let $V_1=729\,mm^3$, $V_2=2744\,mm^3$ and $A_2=393\,mm^2$, because such an object has both volume of $V_2$ and surface area of $A_2$ and $V_2>V_1$. Solve for $A_1$ by plugging in the known values $\Rightarrow (\frac{729\,mm^3}{2744\,mm^3})^{\frac{1}{3}}=(\fra c{A_1}{393\,mm^2})^{\frac{1}{2}}\Rightarrow (\frac{9}{14})(sqrt{393}\,mm)=\sqrt{A_1}\Rightarro w\therefore A_1\approx162.41\,mm^2$.
   August 11th, 2009, 12:12 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,464 Thanks: 2038 2. Similarly, required volume = 500(16/25)^(3/2) in³, etc. (Note: cubed, not squared, since it's a volume.)
  
   Tags geometric, ratios
  
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  # work done by the boy in the given figure is 250 J per second. the speed of the boy is 1.2m/s.what is the force applied by the boy is
  
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   Similar Threads Thread Thread Starter Forum Replies Last Post bilano99 Trigonometry 2 November 12th, 2012 10:56 AM linhbui Elementary Math 4 August 22nd, 2012 06:24 AM jatt-rockz Trigonometry 5 November 10th, 2011 12:17 PM MathematicallyObtuse Algebra 3 January 9th, 2011 08:07 AM MathematicallyObtuse Algebra 4 January 1st, 2011 05:04 PM
  
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explanation: The document is a math forum post that contains two questions about geometric ratios, specifically dealing with the relationship between the volumes and surface areas of similar figures. The post also includes an answer to the first question, but not the second.
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distilabel_metadata.content: My Math Forum Geometric ratios
  
   Algebra Pre-Algebra and Basic Algebra Math Forum
  
   August 10th, 2009, 03:12 PM #1 Newbie   Joined: Aug 2009 Posts: 1 Thanks: 0 Geometric ratios How do I answer these questions? I would like the answer to so I can check the work but I need to know the steps please. 1. The volumes of two similar figures are 729 mm cubed and 2744 mm cubed. If the surface area of the larger figure is 393 mm squared what is the surface area of the smaller figure? 2. The surface area of two figures are 16 in squared and 25 inches squared. If the volume of he larger figure is 500 in cubed, what is the volume of the smaller figure? Answer must be in squared.
   August 10th, 2009, 03:44 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 1. We can determine the surface area of such figure from using the formula of $(\frac{V_1}{V_2})^{\frac{1}{3}}=(\frac{A_1}{A_2})^ {\frac{1}{2}}$, where letting an such object having volume of $V_1$ and surface area of $A_1$, and the other object having volume of $V_2$ and surface area of $A_2$. Let $V_1=729\,mm^3$, $V_2=2744\,mm^3$ and $A_2=393\,mm^2$, because such an object has both volume of $V_2$ and surface area of $A_2$ and $V_2>V_1$. Solve for $A_1$ by plugging in the known values $\Rightarrow (\frac{729\,mm^3}{2744\,mm^3})^{\frac{1}{3}}=(\fra c{A_1}{393\,mm^2})^{\frac{1}{2}}\Rightarrow (\frac{9}{14})(sqrt{393}\,mm)=\sqrt{A_1}\Rightarro w\therefore A_1\approx162.41\,mm^2$.
   August 11th, 2009, 12:12 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,464 Thanks: 2038 2. Similarly, required volume = 500(16/25)^(3/2) in³, etc. (Note: cubed, not squared, since it's a volume.)
  
   Tags geometric, ratios
  
  ,
  ,
  
  ,
  
  ,
  
  ,
  
  # work done by the boy in the given figure is 250 J per second. the speed of the boy is 1.2m/s.what is the force applied by the boy is
  
  Click on a term to search for related topics.
   Thread Tools Display Modes Linear Mode
  
   Similar Threads Thread Thread Starter Forum Replies Last Post bilano99 Trigonometry 2 November 12th, 2012 10:56 AM linhbui Elementary Math 4 August 22nd, 2012 06:24 AM jatt-rockz Trigonometry 5 November 10th, 2011 12:17 PM MathematicallyObtuse Algebra 3 January 9th, 2011 08:07 AM MathematicallyObtuse Algebra 4 January 1st, 2011 05:04 PM
  
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distilabel_metadata.raw_output_q_a_detector_0: The document is a math forum post that contains two questions about geometric ratios, specifically dealing with the relationship between the volumes and surface areas of similar figures. The post also includes an answer to the first question, but not the second.
  
  Label: multiple-question-and-answer