# Show that the sur

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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