Question

Show that the total surface area of a closed cuboid with square base and given volume, is minimum, when it is a cube.(2009)

Answer 1

when 2 cube joins it forms a cuboid so; it is minimum when it is in cube

Answer 2

Let side of the cube is A,A and A respectively.

Let two cube

surface area of both cube is
2×6a^2

2×6×A×A= 12A^2

now joint both cube

it is a cuboid .

Length ,Breadth ,Height of Cuboid are A,A and ×2A

Surface area of Cuboid
= 2( lb×bh×hl)
= 2( A×A + A×2A + 2A×A)

= 2( A^2 + 2A^2 + 2A^2)
= 2(5A^2)
=10A^2



SA of Cuboid (10×) <<<<<<<SA of Cube proved(12×)

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