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Math Help - Prove surface area of cuboid.

  1. #1
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    Prove surface area of cuboid.

    A cuboid has a volume of 8 m^3. The base of the cuboid is square with sides of length x metres. the sureface area of the cuboid is A m^2.
    Show that A=2x^2+\frac{32}{x}
    thanks!
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  2. #2
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    Quote Originally Posted by BabyMilo View Post
    thanks!
    The side lengths are x, x, y.

    The volume is

    V = x^2y

    So 8 = x^2y

    y = \frac{8}{x^2}.


    The surface area is

    TSA = 2x^2 + 4xy

    So A = 2x^2 + 4xy

    A = 2x^2 + 4x\left(\frac{8}{x^2}\right)

    A = 2x^2 + \frac{32}{x}.
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    Quote Originally Posted by BabyMilo View Post
    thanks!
    Please you can leave the question out of quotation tags please? It makes it easier to follow when replying

    What is known:

    Code:
    
    
    
    
    
    V = 8m^3
    square base. 
    
    
    
    
    
    
    A_s = Am^2
    Use the formula for the volume of a cube, given that you have a square base an x^2 term should appear. It will be easiest to introduce a new variable for the height - h in my case.

    Spoiler:
    V = x^2h = 8 \: \: \rightarrow \: \: h = \frac{8}{x^2} where h is the height of the cuboid


    You can now get an expression for the surface area given that it is equal to the sum of it's faces. If you draw a diagram you should be able to find the expression more easily.

    Spoiler:
    A = 2x^2 + 4xh


    You have simultaneous equations to solve now. Eliminate h as it's not being asked for and get the expression for A
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