Question

A cuboid is such that its length is $2$ times the width and the width is $2$ times its height. The side of a square, whose area is equal to the total surface area of the cuboid, in terms of the height of the cuboid is

• A. $4h$
• B. $6h$
• C. $2\sqrt{7}h$
• D. $4\sqrt{7}h$

Answer 1

The correct option is C $2\sqrt{7}h$

Let the height of the cuboid be $h$.

Then, its width $=2h$ and its length $=4h$
$\therefore$ Total surface area
$=2(4h\times 2h+4h\times h\times h\times 2h)$
$=28h^2$ .....(i)
Let the side of the square be $x$.
Then, its area $=x^2$ .....(ii)
From equations (i) and (ii), we have
$x^2=28h^2$
$x=2\sqrt{7}h$