Let k represent the multiplier of the ratio units that will give actual dimensions. The the height can be represented by k, the breadth by 2k, and the length by 3k. The volume of the room will be ...
V = LBH
V = (3k)(2k)(k) = 6k³
3072 m³ = 6k³ . . . . . use known volume
512 m³ = k³ . . . . . . . divide by 6
8 m = k . . . . . . . . . take the cube root
The height of the room is 8 m, its breadth is 16 m, and its length is 24 m.
