Question

If the inner dimensions of a cuboidal box are $50\mathrm{cm}\times 40\mathrm{cm}\times 30\mathrm{cm}$, then the length of the longest rod that can be placed in the box is

• A. $50\mathrm{cm}$
• B. $50\sqrt{2}\mathrm{cm}$
• C. $50\sqrt{3}\mathrm{cm}$
• D. $120\mathrm{cm}$

Answer 1

The correct option is B

$50\sqrt{2}\mathrm{cm}$

Step 1: Given data

The inner dimensions of a cuboidal box are:

$l=50\mathrm{cm},b=40\mathrm{cm},c=30\mathrm{cm}$,

Step 2: Determining the length of the longest rod

Length of longest rod= length of diagonal

For cuboid with dimensions, $50\mathrm{cm}\times 40\mathrm{cm}\times 30\mathrm{cm}$,

The length of the diagonal is $=\sqrt{l^2+b^2+c^2}$

$$\begin{gathered} =\sqrt{l^2+b^2+h^2} \\ =\sqrt{(50{)}^2+(40{)}^2+(30{)}^2} \\ =50\sqrt{2}\mathrm{cm} \end{gathered}$$

Hence, length of the longest rod will be $=50\sqrt{2}cm$