Draw the vertical "height" line down the middle of the triangle.
From the center of the circle, draw radius lines to the two base vertices of the triangle. Label the three radius lines (the two you've just drawn, plus the one that coincides with part of the "height" line) as "R".
Label the cone's radius as "r", and the remaining part of the height of the cone as "h". Using Pythagorus, note that r = sqrt[R^2 - h^2].
Plug "4" in for "V" in the formula for the volume of a sphere. Solve the resulting literal equation for R.
Take the formula for the volume of a cone with radius "r" and height "h". Plug in "sqrt[R^2 - h^2]" for "r^2" in this formula. Subtitute for the R, using what you got from the previous step.
You should, I believe, now have the volume of the cone expressed only in terms of the height h. Maximize.
Label the height as "h = 2", with dh/dt = 0. Label the distance between the boat and the dock as "x", with dx/dt = -0.1. Then the rope's length is clearly D = sqrt[4 + x^2]".
Differentiate the equation for the rope's length with respect to time "t". Plug in the known values, and solve for dD/dt.
If you get stuck, please reply showing how far you have gotten. Thank you!