# CLASS-9VOLUME & SURFACE AREA OF THE SOLIDS -DIAGONAL OF CUBOID

DIAGONAL OF CUBOID -

Cuboid A rectangular solid bounded by six rectangular plane faces is called a cuboid. A match box, a chalk box, a brick, a block, a book, etc., are all examples of a cuboid. A cuboid has 6 rectangular faces, 12 edges and 8 vertices. Let us considered a cuboid of length = l units, breadth = b units, and height = h units. Diagonal of a Cuboid

The line joining (red coloropposite corners of a cuboid is called its diagonal. A cuboid has four diagonals. A diagonal of a cuboid is the length of the longest rod that can be placed in the cuboid.

Diagonal of cuboid = √l² + b² + h² units

Example.) Find the length of the longest rod that can be placed in a room 15 m long, 16 m broad, and

2

10 ------ m high.

3

2          32

Ans.) Here, l = 15 m, b = 16 m, h = 10 ------ = ------- = 10.67 m

3           3

Length of the longest rod = Length of Diagonal

=  √l² + b² + h²

=  √(15)² + (16)² + (10.67)²

=  √225 + 256 + 113.85

=  √594.85 = 24.4 m        (Ans.)