calculus

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Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6.
y = 6 − x
y = 0
y = 5
x = 0

  • calculus -

    You can use shells:

    The region has to be broken up into the constant-height region where 0<=x<=1 and the slanting region where 1<=x<=6:

    V = 2pi*Int(r*5 dx)[0,1] + 2pi*Int(rh dx)[1,6]
    where r = 6-x
    h = 6-x
    = 138 2/3 pi

    Or, using discs,

    V = pi*Int(6^2 - y^2) dy[0,5]
    = 138 2/3 pi

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