Question

The length, breadth and height of a rectangular room are in the ratio of 3:2:1. If the room contains 3072 cubic meter of air, find the length, breadth and height of the room.​

Answer 1

See below ↓↓↓

Explanation:

Given :

• Length, breadth, and height in the ratio 3 : 2 : 1
• Room contains 3072 cubic meter of air [refers to volume]

Solving :

• Let the length, breadth, and height be 3x, 2x, and x respectively
• Multiply them and equate to the volume
• (3x)(2x)(x) = 3072
• 6x³ = 3072
• x³ = 512
• x = 8

Solution :

• Length = 3x = 24 m
• Breadth = 2x = 12 m
• Height = x = 8 m

Answer 2

• length: 24 m
• breadth: 16 m
• height: 8 m

Explanation:

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.