The breadth of a room is twice its height, one half of its length and

1.	The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. Dm. Find its dimensions.
Answer» Given, Breadth of room is twice of its height, b = 2h or h = b/2 … (i) Breadth is one half of length, b = l/2 or l = 2b … (ii) Volume of the room = lbh = 512 dm³ … (iii) By substituting (i) and (ii) in (iii) 2b × b × b/2 = 512 b³ = 512 b = ³√(512) = 8 ∴ Breadth of cube = b = 8 dm Length of cube = 2b = 2×8 = 16 dm Height of cube = b/2 = 8/2 = 4 dm

The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. Dm. Find its dimensions.

Answer»

Given,

Breadth of room is twice of its height, b = 2h or h = b/2 … (i)

Breadth is one half of length, b = l/2 or l = 2b … (ii)

Volume of the room = lbh = 512 dm³ … (iii)

By substituting (i) and (ii) in (iii)

2b × b × b/2 = 512

b³ = 512

b = ³√(512)

= 8

∴ Breadth of cube = b = 8 dm

Length of cube = 2b = 2×8 = 16 dm

Height of cube = b/2 = 8/2 = 4 dm