Find the dimensions of the right circular cylinder of maximum volume that can be inscribed in a sphere of radiusa

so for the main equation that we will differentiate, i determined that

V(of cylinder) = (pi)(r^2)(h)

and for the connector, i made the picture of the spere and the cylinder flat so that it was two-dimensional and it became a rectangle inscribed in a circle.

i looked at this picture and decided that i had to somehow connect the cylinder to the sphere so i decided to use the equation of a circle as a connector(was this right?)

connector: r^2= x^2 + y^2

from there i found that y=(r^2-x^2)^(1/2) for later use

after this i dont even know where i went....i think i accidentally mixed up some x's and y's that i labeled before and got an illegitimate answer. so basically im confused.

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