Question

The volume of a cuboid whose sides are in the ratio $1:2:4$ is same as that of a cube. What is the ratio of the length of diagonal of the cuboid to that of the cube?

• A. $\sqrt{1.25}$
• B. $\sqrt{1.75}$
• C. $\sqrt{2}$
• D. $\sqrt{3.5}$

Answer 1

The correct option is B $\sqrt{1.75}$

Let length, $l=x,$ breadth$=2x$, height$=4x$

Volume of cuboid$=lbh=x\times 2x\times 4x=8x^3$

Let edge of cube be 'a'

Volume of cube=Volume of cuboid

$a^3=8x^3\Rightarrow a=2x$

Diagonal of cuboid$=\sqrt{l^2+b^2+h^2}=\sqrt{x^2+4x^2+16x^2}$

$=\sqrt{21x^2}=x\sqrt{21}$

Diagonal of cube$=\sqrt{a^2+a^2+a^2}=\sqrt{4x^2+4x^2+4x^2}$

$=x\sqrt{12}$

$\therefore \frac{Diagonalofcuboid}{Diagonalofcube}=\frac{x\sqrt{21}}{x\sqrt{12}}=\sqrt{1.75}$