Question

Prove that a conical tent of given capacity will require the least amount of canvas when the height is √2 times the radius of the base.

Answer 1

Suppose the radius and height of cone be r and h respectively

Given as the volume of cone is fixed.

Volume of the cone, V = (1/3)πr²h

h = 3V/πr² ...(1)

The curved surface area of cone, S = πrl(l is the slant height)

Here,

Condition for the maxima and minima is