Question

The dimensions of a box are 12 cm X 4 cm X 3cm .Find the length of the longest rod which can be placed in this box.

Answer 1

Given :-

• Dimensions of the box = 12cm × 4cm × 3cm

Aim :-

• To find the length of the longest rod which can be placed in the box

Formula to use :-

The length of the longest rod which can be placed in the box must be placed diagonally in order to be the longest.

To find the length of this rod,

$\longrightarrow \sf \sqrt{(length)^{2} + (breadth)^{2} + (height)^{2}}$

Substituting the values,

$\implies \sf \sqrt{(12)^{2} + (4)^{2} + (3)^{2}}$

$\implies \sf \sqrt{144 + 16 + 9}$

$\implies \sf \sqrt{169}$

$\implies\sf 13$

Hence, the length of the longest rod which can be placed in the box is 13cm.

Some more formulas :-

• Total surface area of a cuboid = 2 ×[(length + breadth) + (breadth + height) + (height + length)]
• Lateral surface area of a cuboid = 2 × height + length + 2 × height × breadth ⇒ 2 × height (length + breadth)
• Volume of a cuboid = Length × Breadth × Height
• Length of the longest rod which can be placed in a cube = √3 × side

Answer 2

Answer:

Step-by-step explanation:

Given that:

length l=12m

breadth b=4m  

height h=3m

Longest rod that can be placed in a room is nothing but its diagonal.

Length of diagonal of a cuboid= sqrt(l^2 +b^2 +h^2)

Length of longest rod = sqrt(12^2 +4^2 +3^2)

                                    = sqrt(144+16+9)

                                    = sqrt169 = 13

So, the length of the longest rod is 13m.