Show that the right circular cone of least curved surface and given volume has an altitude equal to `sqrt2` time the radius of the base.

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#### Solution

Let* r *and *h* be the radius and the height (altitude) of the cone respectively.

Then, the volume (*V)* of the cone is given as:

V=13πr2h⇒h=3Vπr2

The surface area (*S) *of the cone is given by,

*S* = π*rl* (where *l* is the slant height)

Hence, for a given volume, the right circular cone of the least curved surface has an altitude equal to `sqrt2` times the radius of the base.

Concept: Maxima and Minima

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