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Math Help - proportions

  1. #1
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    proportions

    ok so here we go....

    for any cube, if the volume is V cubic inches and the surface area is A square inches, then V is directly proportional to which of the following

    a. A

    b. A^2

    c. A^3

    d. A^(2/3)

    e. A^(3/2)


    so in this problem am i to compare volume to surface area?

    or say that volume is proportional to surface area?

    V^3 = K*A^2

    but in a cube and square the lengths are the same, right?

    so I can say A^3 = K*A^2?

    i dunno this setup seems wrong, but im not seeing where i am making the mistake...

    k in this problem is the proportion constant.....
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  2. #2
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    Re: proportions

    Yes, in a cube and a square which is a face of the same cube, the side length is the same. Use that side length, s, as the "connection". The volume is proportional to s^3: V= s^3. And the area is proportional to the area: A= s^2. Eliminate s from those two equations to get a formula in only V and A.

    (And what you give: V^3= kA^2 does NOT say "volume is proportional to area", it says "volume cubed is proportional to area squared".)
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  3. #3
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    Re: proportions

    ok so s = V^(1/3) and s = A^(1/2)...

    ok so V^(1/3) = K*A^(1/2)

    ok so V = k*A^(3/2). thanks!
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  4. #4
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    Re: proportions

    Yes. You could also have reasoned that s= A^(1/2) so V= s^3= (A^(1/2))^3= A^(3/2). Notice that here k happens to be 1. It is, in fact, true for any object that the volume is proportional to the surface are to the 3/2 power. For a cube the constant of proportionality is 1.
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