Question

Raju has 64 small cubes of $1c{m}^3$. He wants to arrange all of them in a cuboidal shape, such that the surface area will be minimum. What is the diagonal of this larger cuboid ?

• A. $4\sqrt{3}cm$
• B. $2\sqrt{3}cm$
• C. $4cm$
• D. $2cm$

Answer 1

The correct option is A $4\sqrt{3}cm$

Volume of each cube is $1c{m}^3$$(Length\times Width\times Height)$$or\left(lbh\right)$. All sides of a cube are equal and hence side of cube is 1cm. Surface area will be maximum when the complete arrangement forms a cube. To form a cube from all the 64 cubes, let side of the cube is $xcm$. Volume of final cube should be equal to $64c{m}^3$. So $x^3=64c{m}^3$ and hence, $x=4cm$. So, now diagonal of this large cube $x\sqrt{3}cm$i.e., $4\sqrt{3}cm$