Expressions of volume and surface areaNow I understand that the volume of a cuboid is V = w h d but what I am struggling with is the following:If w and d are both equal lets call them x, then how can I find an expression for h in terms of x? The closest I can get is h = V / x 2 Is this correct?In continuation how would I go about finding the surface area A in terms of x only using the answer from the first question?

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Expressions of volume and surface areaNow I understand that the volume of a cuboid is   V  =  w  h  d but what I am struggling with is the following:If w and d are both equal lets call them x, then how can I find an expression for h in terms of x? The closest I can get is  h  =  V      /        x    2  Is this correct?In continuation how would I go about finding the surface area A in terms of x only using the answer from the first question?

Allyson Vance · Accepted Answer

Step 1Yes, that is correct.The surface area of a cuboid with dimensions w, h, d is   A  =  2  (  w  h  +  w  d  +  h  d  ).This can be seen by computing the area of each of the faces of the cuboid and the adding them.Step 2In your example, this reduces to   A  =  2  (  x  h  +      x    2    +  h  x  )  =  2      x    2    +  4  x  hNow, the question asks that you express this in terms of x (not in terms of x only) using the equation from the first question, i.e.   h  =      V          x      2      . So we substitute this expression for h into the equation for the area to get   A  =  2      x    2    +  4  x      V          x      2        =  2      x    2    +  4      V    x

Now I understand that the volume of a cuboid is V = whd but what I am struggling with is the following: If w and d are both equal lets call them x, then how can I find an expression for h in terms of x?

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