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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.

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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 = 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.

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APPEARS IN

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