Find the length of the longest rod that can be placed in a room of dimensions 30m x 24m x - Maths - Surface Areas and Volumes

Question

Find the length of the longest rod that can be placed in a room
of dimensions 30m x 24m x 18m

Vimala · Accepted Answer

The dimensions of the room are $30 m \times 24 m \times 18 m$ .

We need to find the length of the longest rod that can be placed in the above mentioned room.

In a cuboid, the diagonal is longest line that can be fixed in.

The diagonal of the cuboid is $\sqrt{a^{2} + b^{2} + c^{2}}$ , where a, b, c are the dimensions of the cuboid.

Let us find the diagonal of the room:

$d = \sqrt{30^{2} + 24^{2} + 18^{2}} = \sqrt{900 + 576 + 324} \approx 42.43 m$

Thus the length of the rod that can be fixed in the room is 42.43m

Find the length of the longest rod that can be placed in a room of dimensions 30m x 24m x 18m.