Question

If the dimensions of a cuboid are $5$ cm$\times$ $4$ cm $\times$ $3$ cm, then find the maximum volume of the cube that can be carved of it. (in $c{m}^3$).

• A. $24$
• B. $27$
• C. $30$
• D. $33$

Answer 1

The correct option is B $27$

Volume of cuboid=$length\ast breadth\ast height$.

Volume of cube=$sid{e}^3$ (since length,breadth and height are same)

The dimensions of the cuboid that is given are $5,4and3.$

In order to carve a cube out of a cuboid all the sides have to be equal.

The volume of the cube has to be the MAXIMUM volume that can be carved in.

All the either can be $5$ or $4$ or $3$. It cannot be $5$ because other sides are less that $5$. They cannot be extended. It cannot be $4$ either bacause the third dimension is less than $4$ that is $3$. So all the dimensions of the cube have to be $3cm$

Therefore the maximum volume of the cube that can be carved of it is

$\Rightarrow 3\ast 3\ast 3=27c{m}^3$