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Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is
.
Asked by Srikumar Last Modified
Answer A sphere of fixed radius (r) is given.
Let R and h be the radius and the height of the cone respectively.
The volume (V) of the cone is given by,
Now, from the right triangle BCD, we have:
∴h
∴ The volume is the maximum when
Hence, it can be seen that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is.
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