Question

Find the length of the longest rod which can be fit in the cuboidal room of dimension 6m times5m times4m​

Answer 1

Given :

• Length of the cuboidal room = 6 m
• Breadth of the cuboidal room = 5 m
• Height of the cuboidal room = 4 m

To find :

• Length of the longest rod which can fit in the cuboidal room

Concept :

Length of the longest rod = Diagonal of the cuboid

So, to find the length of the longest we need to find the diagonal of the cuboidal room. The resultant value after substituting the given values will be our required answer.

Formula to calculate diagonal of cuboid :-

• Diagonal of cuboid = √(l² + b² + h²)

where,

• l stands for the length
• b stands for the breadth
• h stands for the height

Solution :

Calculating the length of the longest rod :-

→ Diagonal = √(l² + b² + h²)

→ Diagonal = √((6)² + (5)² + (4)²)

→ Diagonal = √(36 + 25 + 16)

→ Diagonal = √77

→ Diagonal = 8.78

Therefore,

• Length of the longest rod which can fit in the cuboid room of dimension 6 m × 5 m × 4 m is 8.78 m

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KNOW MORE :

• Total surface Area of cuboid = 2(lb + bh + hl)
• Volume of cuboid =  length × breadth × height
• Perimeter of cuboid = 4 (length + breadth + height)
• Total surface area of cube = 6 × side²
• Volume of cube = side³
• Perimeter of cube = 12 × side