Q. 264.8( 4 Votes )

Show that the sur

Answer :

Let us assume that the square base has side x and height h.

Let us assume that given volume of the cuboid is V.


V = x2h


h = V/(x2)


Now surface area of the cuboid is-


S = 2x2 + 4xh


= 2x2 + 4x[V/(x2)]


= 2x2 + 4(V/x)


On differentiating S, we get-



To find critical points,







Taking second derivative of S, we get-




Hence, is a point of minimum.




Thus, the surface area and volume is minimum when h = x which implies that cuboid is a cube.


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