Question

The edge of a cube is 5 cm. Find the longest rod which

can be placed in it.​

Answer 1

$\sf\huge\underline{Explanation :-}$

Given :

• Edge of a cube = 5 cm

To find :

• Longest rod which can be placed in it.

Solution :

Here, the edge of the cube is 5 cm.

The length of the longest rod which can be placed in it is equal to the length of the diagonal of the cube.

We know that,

Diagonal of a cube = √3 × a unit

[where a is one edge of the cube.]

= 5 × √3 unit

.°. Diagonal = 5√3 cm

Hence, the length of the longest rod which can be placed in the cube is 5√3 cm respectively.

$\sf\huge\underline{Extra \: information :-}$

• A cube has 6 surfaces. Hence, total surface area of the cube is = 6a² sq. unit [where a is one side of the cube.]
• The formula of finding the volume of the cube is = a³ cu. unit

Answer 2

$\huge{ \underline{ \rm{Answer-}}}$

The longest rod which can be placed in the cube is of $5 \sqrt{3} \: cm$

$\huge{ \underline{\rm{ \blue{Explanation:- }}}}$

Given :- Edge of cube is 5 cm.

To find :- Longest rod which can be placed in the cube.

Now,

Edge of cube = 5cm

Then, length of rod = diagonal of cube.

Now, Diagonal of cube =$\bold \red{ \sqrt{3} \times side}$

$= (5 \times \sqrt{3} )cm$

$= 5 \sqrt{3} \: cm$

Hence, the longest rod which can be placed in the cube is $\bold \red{5 \sqrt{3} \: cm}$