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By what factor help?

  1. Apr 10, 2017 #1
    1. The problem statement, all variables and given/known data
    pipe factor question.PNG cake volume.PNG

    2. Relevant equations
    Cake one...
    Area of circle times height
    Pipe one... Av = Av

    3. The attempt at a solution
    Hello, i would like some help in the right direction/
    I had a go at these problems and got B) for the pipe one and C for the cake one.
    However the correct answers for the pipe one is A) whereas the one for the cake is E.).

    I dont understand what im doing wrong. If you try substituting values and work backwards the constants i get dont fit.
    EG: for the pipe one i made r = 4...
    pi * 4^2 * 0.5 = pi* x * 4^2 * 2
    x = 0.25 so i got B, but the correct answer is A...

    For the cake problem i made h=5 and diametre = 8cm (radius = 4)...
    pi * 4^2 * 5 = 251 m-3
    i then doubled volume, and worked backwards to find factor to increase radius and therefore diamtre by...

    502 = pi * r^2 * 5
    r = 5.6418
    5.6418/4 = 1.44... so i got C, but correct answer is E

    Please help me
     
  2. jcsd
  3. Apr 10, 2017 #2
    Pipe: if x is the scaling of the radius, you should have pi*x^2*4^2*2
    Cake: it is a scale model, so all dimensions increase by the same factor: pi*x^2*4^2*x*5 = 502
     
  4. Apr 10, 2017 #3
    Hello, thank you so much!! I get the one with the pipe, but i dont quite get the second one, where did the other x come from? Do you have a site i can read up on to explain this i'm too stupid.
     
  5. Apr 10, 2017 #4

    haruspex

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    It says it is a scale model, so all dimensions increase in the same ratio. If the cake starts with radius r and height h, and all dimensions are scaled up by a factor x, what is the new radius? What is the new height? What is the new volume?
     
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