Solution Let OC = r be the radius of the cone and OA = h be its height Let a cylinder
with radius OE = x inscribed in the given cone (Fig 6 18) The height QE of the cylinder
is given by
Rationalised 2023-24
APPLICATION OF DERIVATIVES
171
QE
OA  = EC
OC    (since ∆QEC ~ ∆AOC)
or
QE
h  = r
x
r
−
or
QE =
(
)
h r
x
r
−
Let S be the curved surface area of the given
cylinder