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How will you arrange 12 cubes of equal lengths to form a cuboid of smallest surface area? 

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Best answer

We can’t obtain the least total surface area by arranging 12 cubes by side by side.

∴ A = 2(lb + bh + lh)

= 2(12 × 1 + 1 × 1 + 12 × 1)

= 2(12 + 1 + 12)

= 2 × 25 = 50 Sq. cm.

We can obtain the least total surface area by arranging 3 cubes by 4 cubes.

∴ A = 2(lb + bh + lh)

= 2(3 × 1 + 1 × 4 + 3 × 4) (∵ l = 3; b = 1; h = 4)

= 2(3 + 4 + 12)

= 2 × 19

= 38 Sq. cm.

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