Question

A cuboid has edges of $x$ cm, $1cm$ and $2cm$. The total surface area of the cuboid has a numerical value which is some integral multiple of the numerical values of its volume. What is the value of $x$ for minimum possible positive integral multiple ?

• A. $5cm$
• B. $2cm$
• C. $3cm$
• D. $4cm$

Answer 1

The correct option is B $2cm$

Total surface of the cuboid $=2(x+2+2x)$
$=6x+4$
Volume of the cuboid $=l\times b\times h$
$=x\times 1\times 2=2x$
Given, $6x+4=n\times 2x$ , where n is an ingeger
$=>(2n-6)x=4$
Since $x$ is the length of the cuboid and length cannot be negative,
$\therefore x(2n-6)>0$ or $2n>6$ or $n>3$
$n$ is positive integer, minimum value of $n=4$
$=>6x+4=2\times 4x$
$=>x=2cm$.