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 $h$ of the cuboid, is

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

Answer 1

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

Let height of cuboid $=h$, $\therefore$ width$=2h$, length $=4h$
Surface Area $=2(2h^2+8h^2+4h^2)=28h^2$
Area of square$=a^2\Rightarrow a^2=28h^2$
$\Rightarrow a=2\sqrt{7}h$