Question

Find the volume of the largest right circular cone that can be inscribed in a sphere of
radius r.

Answer 1

volume of cone is
\[V = \frac{\pi}{3} x^2 h\]
h = r+y
and
x^2 + y^2 = r^2 or x^2 = r^2 - y^2
\[\rightarrow V = \frac{\pi}{3} (r^2 -y^2)(r+y)\]
maximize volume by differentiating with respect to "y" and setting equal to 0