text: # The surface area of a cuboid is 1400cm^2, ratio of edges is 2:3:4. Calculate the volume of the cuboid.
  
  The surface area of the cuboid is `1400cm^2.`
  
  Since the ratios of the edges are 2:3:4 then letting x represent the factor, the sides have length 2x, 3x, and 4x.
  
  Therefore the surface area of the cuboid can be represented by:
  
  `2(8x^2) + 2(6x^2) + 2(12x^2)`
  
  `16x^2 + 12x^2 + 24x^2`
  
  `52x^2` = `1400`
  
  ` ` `x^2 = 1400/52`
  
  `x =sqrt(1400/52)`
  
  `x =sqrt(350/13)`
  
  Each side of ratio 2:3:4 is:`2sqrt(350/13)` , `3sqrt(350/13)` , and `4sqrt(350/13)`
  
  Therfore to find the volume of the cuboid: length x width x height is:
  
  `2sqrt(350/13)* 3sqrt(350/13)* 4sqrt(350/13)` = `2*3*4* sqrt(350/13)^(3)`
  
  `12(350/13)*sqrt(350/13)`
  
  `4200/13*sqrt(350/13)`
  
  If I rationalize the denominator for `sqrt(350/13)`  I get `sqrt(4550)/13`
  
  `4200/13*sqrt(4550)/13` = `(4200sqrt(4550))/169` `~~` 1676.364 `cm^3`
  
  The volume of the cuboid is approximately 1676.364 cubic centimeters.
  
  Approved by eNotes Editorial Team
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