Question

What is the length of the greatest rod that can be placed in a room whose length is 10 meter, breadth 8 meter and height 6 meter?
Given that \[\sqrt 2 = 1.42\]

Answer 1

Hint: We have to find the length of a longest rod means the longest distance in a room. As it is given that the rod is to be placed in a room and room is in the form of a cuboid so the longest length of a rod in the cuboid will be a diagonal of the cuboid. So, we will find the value of the diagonal of the cuboid.

Complete step-by-step solution:
Given: length of the room is 10 m.
The breadth of the room is 8 m.
Height of the room is 6 m.
The room is in the shape of a cuboid. So, these dimensions are of a cuboid.
Now, in the question it is asked that we have to fit the longest rod in the cuboid. It means we need to find the space in a cuboid which can accommodate the longest rod.
In a cuboid, the longest length is the diagonal of a cuboid. So, if we know the diagonal of a cuboid we can fit the longest pole there.
So, we will find the value of the diagonal of the cuboid.
Formula to find the diagonal of a cuboid whose length, breadth and height is given is $\sqrt {{l^2} + {b^2} + {h^2}} $. Here, l is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid.
Substituting the values in the formula.
Diagonal of cuboid $ = \sqrt {{{10}^2} + {8^2} + {6^2}} $
$ = \sqrt {100 + 64 + 36} $
$ = \sqrt {200} $
$ = \sqrt {2 \times 100} $
Square root of 100 is 10. So, we will write it as 10.
$ = 10\sqrt 2 $
Value of $\sqrt 2 $ is given in the question. so, substituting it with that value.
$ = 10 \times 1.42$
$ = 14.2m$
So, the longest rod which can fit in the room is 14.2 meter long.

Note: Always write the units of the lengths in the solution. We should not get confused between cube and cuboid. We know that the faces of a cuboid are parallel to each other. Unlike the cube, the sides of the cube are not equal. The length of all the edges of the cube is equal to each other but it does not happen in a cuboid. The Cube is the most symmetric in all hexahedron shaped objects. The diagonals of the cube are identical to each other but the diagonals of a cuboid are not equal.