Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.

A classroom is 7 m long, 6 m broad and 3.5 m high. Doors and windows occupy an area of 17 m². What is the cost of white washing the walls at the rate of Rs. 1.50 per m².

The central hall of a school is 80 m long and 8 m high. It has 10 doors each of size 3 m ×1.5 m and 10 windows each of size 1.5 m× 1 m. If the cost od white washing the walls of the hall at the rate of Rs. 1.20 per m² is Rs. 2385.60, find the breadth of the hall.

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that

The areas of three adjacent faces of a cuboid are x, y, and z. If the volume is V, prove that V₂ = xyz.