Question

find the length of longest pole that can be put in a room of dimensions 10m×6m×4m.​

Answer 1

GiveN :

• Length of the room = 10 m
• Breadth of the room = 6 m
• Height of the room = 4 m

To Find :

• Length of the longest pole that can be put in a room.

Calculation :

Supposition: Let us suppose the room as a cuboid means like a cuboidal shape.

Knowledge required :

• Whenever we are asked to find the length of longest pole of a room with dimensions provided (length × breadth × height), in this case, we simply need to assume that we have to calculate the diagonal of cuboidal room.

So, let's calculate the diagonal of a cuboidal room,

$\dag$ Formula -

$\underline{ \boxed{ \tt{Diagonal_{(Cuboid)} = \sqrt{l^2 + b^2 + h^2} }}}$

Where,

• Length = 10 m
• Breadth = 6 m
• Height = 4 m

So, as per the formula, let us insert the values in the equation,

$\longrightarrow \rm Diagonal_{(Cuboid)} = \sqrt{l^2 + b^2 + h^2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \rm Diagonal_{(Cuboid)} = \sqrt{10^2 + 6^2 + 4^2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \rm Diagonal_{(Cuboid)} = \sqrt{(10 \times 10) + (6 \times 6) + (4 \times 4)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \rm Diagonal_{(Cuboid)} = \sqrt{100 + 36 + 16}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \rm Diagonal_{(Cuboid)} = \sqrt{152}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow{ \underline{ \boxed{\rm{ \red{ Diagonal_{(Cuboid)} = 12.32 \: m}}}}}$

Therefore,

• The length of longest pole that can be put in a room is 12.32 m. ⠀⠀

Answer 2

Given :

• Dimensions of Room are 10m × 6m × 4m.

To find :

• Length of the longest pole

Solution :

• In the question dimensions of the Room are 10m × 6m × 4m. So it is asked to find the length of the longest pole. so We will find the diagonal of the room

✰ Length (L) = 10m

✰ Breadth (B) = 6m

✰ Height (H) = 4cm

Let's Find out..!

Diagonal = √L² + B² + H²

⟹ √(10)² × (6)² + (4)²

⟹ √100 + 36 + 16

⟹ √136 + 16

⟹ √152

⟹ 12.32 m

∴Length of longest Pole is 12.32m.

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