Q. 19

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 :

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

It is given that volume of cone is fixed.

Volume of cone, V =

h = …1

Curved surface area of cone, S = πrl (l is slant height)



Condition for maxima and minima is


For , > 0

S will be minimum for

From equation 1

(from equation 3)

h = √2 r

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