# Show that the Right Circular Cone of Least Curved Surface and Given Volume Has an Altitude Equal to Time the Radius of the Base. - Mathematics

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.

#### 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 = πrl (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.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 24 | Page 233