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I Volume of a Frustum

  1. Feb 18, 2017 #1
    The question is as follows:

    Using all your Calculus knowledge, develop and justify, a formula for the rate of change of the heigh of a liquid in the cup, give:
    - The machine pours the liquid at a constant rate - ie. flow rate is constant
    - The shape of the cup is a "frustum", as given in the diagram
    - No liquid is spilt during pouring

    No values are given.

    top radius = b
    bottom radius = a
    liquid radius = r

    liquid height = h
    frustum height = H
  2. jcsd
  3. Nov 26, 2017 #2
    The equation to find the volume of frustum is ,
    V=pi/3 * (a^2+b^2+ab)H
    And you can use the similarity relations to get an equation relating the upper radius of the water column and the water height h.
    substitute this relation in the V=qt relation (where q is the volume flow rate).
    I hope you will do the differentiation part.
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