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A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2. What are the dimensions of such a cylinder which has maximum volume?



  • Calculus -

    did you make a sketch??
    let the radius of the cylinder be r
    let the height of the cylinder by h

    by similarity I can set up the ratio h/(2-r) = 8/2
    ---> h = 8-4r

    volume of cylinder
    = pi(r^2)(8-4r)
    = 8pi(r^2) - 4pi(r^3)

    differentiate, set equal to zero, solve for r, etc

    (I got r = 4/3)

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