Question

A box measures $30$ cm $\times 24$ cm $\times 18$ cm.The longest rod that can be placed in it has the length

• A. $16$ cm
• B. $30$ cm
• C. $42.42$ cm
• D. $42.52$ cm

Answer 1

The correct option is C $42.42$ cm

The dimensions of the cube are $30\times 24\times 18$
The longest rod that can be placed in the box will have length equal to the one which joins the opposite ends of thee box. Hence, length of rod = $\sqrt{(l^2+b^2+h^2)}$
$=$ $\sqrt{\left(\right(30{)}^2+(24{)}^2+(18{)}^2)}$
$=$ $\sqrt{1800}$
$=42.42$ cm