Suppose r be the radius of base circle of the cone, l be the slant length and h be the height of the cone
Let us assume be the semi - vertical angle of cone.
As we know that volume of a right circular cone is given by
From the cross-section of the cone, we see that
Let us consider S as a function of R and to find the value of r for it's extremum,
Differentiate S with respect to r, we get
On equating differentiate to zero to get the relation between h and r
Since, the remainder > 0 only the remainder gets equal to zero.
