Find the dimensions of the largest right circular cylinder that can be inscribed in a sphere of radius 6 inches.

Answer 1

Draw a side view. If the cylinder has radius r, and height h, then

r^2+h^2 = 6^2
the volume of the cylinder is thus

v = πr^2h = πr^2√(36-r^2)

now just find dv/dr=0 and thus the maximum volume's radius.

Answer 2

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