Question

The areas of three adjacent faces of a cuboid are $a,b$ and $c$. If the volume of the cuboid is $V$, then what is $V^2$ equal to

• A. $abc$
• B. $ab+c$
• C. $a+b+c$
• D. None of these
  

Answer 1

The correct option is A $abc$

Let the length breadth and height of the cuboid be $x,y$ and $z$ units respectively.
Then $x\times y=a,y\times z=b,x\times z=c$
$\therefore x\times y\times y\times z\times x\times z=a\times b\times c$
$\Rightarrow x^2{y}^2{z}^2=abc$
$\Rightarrow {\left(xyz\right)}^2=abc$
$\Rightarrow V^2=abc$