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Math Help - box volume/surface area

  1. #1
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    box volume/surface area

    A box with a volume of 400 cm^{3} has the shape of a rectangular prism. It has a fixed height of 25 cm, a length of y cm and a width of x cm. If A cm^{2} is the total surface area:
    a) Express A in terms of x.

    I don't understand what it means when it says 'express A in terms of x'. Anyway if someone could provide detailed working out to this it will be appreciated!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    They want a formula for the Surface area that has nothing but x's in it.

    Example:

    Perimiter is p=2x+2y. If y=2x+6, then p expressed in terms of x is p(x)=2x+2(2x+6).
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  3. #3
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    e^(i*pi)'s Avatar
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    Express A in terms of x means A = some function of x. In other words it doesn't want any y in there

    The volume of a cuboid (a rectangular prism is a cuboid) is V = xyz. You are given V = 400 and z = 25

    The surface area of a cuboid is 2(xy+yz+xz) (in other words the sum of the six faces)

    From the expression for volume you get 16 = xy (eq1)

    and from the expression for area: A = 2(xy+25y+25x) (eq2)

    You can use eq1 to eliminate y in eq2
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  4. #4
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     <br />
V=xyz<br />

     <br />
V=400, z=25<br />

     <br />
xy=16, y=\frac{16}{x}<br />
    A= 2(xy+25y+25x) <br />
=32+50y+50x<br />
=32+50(\frac{16}{x}) +50x<br />
     <br />
A=32+\frac{800}{x}+50x<br />
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  5. #5
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    Thanks for the help VonNemo19 and e^(i*pi)!

    Incidentally, do you guys think that it's beneficial to memorise all these equations we use in geometry (i.e. the surface area of a cuboid, volume of a sphere, volume of cylinder etc)? Generally is it recommended that people memorise all of these equations?
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  6. #6
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Joker37 View Post
     <br />
V=xyz<br />

     <br />
V=400, z=25<br />

     <br />
xy=16, y=\frac{16}{x}<br />
    A= 2(xy+25y+25x) <br />
=32+50y+50x<br />
=32+50(\frac{16}{x}) +50x<br />
     <br />
A=32+\frac{800}{x}+50x<br />
    Yes that's correct

    Quote Originally Posted by Joker37 View Post
    Thanks for the help VonNemo19 and e^(i*pi)!

    Incidentally, do you guys think that it's beneficial to memorise all these equations we use in geometry (i.e. the surface area of a cuboid, volume of a sphere, volume of cylinder etc)? Generally is it recommended that people memorise all of these equations?
    I tend to think of them logically. For example the volume of a prism is V = A_Ch where A_C is cross sectional area and h the height. For a cylinder the cross section is a circle and for a cuboid it's a rectangle both of who's areas are easy to work out.

    Surface area is a logical one for me, in this problem I imagined a rectangle which will have 3 pairs of faces (hence the 2 outside the brackets) and those faces are simply squares.

    The only ones I tend to remember are:

    V_{sphere} = \dfrac{4}{3}\pi r^3

    A_{sphere} = 4\pi r^2

    V_{cone} = \dfrac{1}{3}Ah where A is the area of the base and h the perpendicular height from the apex.


    edit: I should mention that in some exams you are given certainly formulae, make sure you know what these are so you don't have to remember them, just what they do
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