Q24 of 33 Page 6

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. (CBSE 2011,2013)


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)


Since,





So,



Condition for maxima and minima is






…2



For , > 0


S will be minimum for


From equation 1


(from equation 3)


h = √2 r

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