Question

The breadth of a room is twice its height and is half of its length. The volume of room is 512 dm²
Its dimensions are
(a) 16 dm. S dm. 4 dm (b) 12 dm. 8 dm. 2 dm
(c) S dm. 4 dm, 2 dm
(d) 10 dm. 15 dm. 20 dm
-
​

Answer 1

First of all, volume is always measure in unit³ not in unit².

So, the correct question is_

The breadth of a room is twice its height and is half of its length. The volume of room is 512 dm³.

Let's do the calculation now:

Let, the breadth be, 'x'

So, according to the question,

The height of the room is = (x/2)

The length of the room is = (x*2)

                                          = 2x

So, the volume of the room is = (2x*x*x/2)

                                                = x³

According to the problem,

x³ = 512

⇒ x =∛512

⇒ x =∛(8)³

⇒ x = 8

So, the breadth of the room is 8 dm

The length of the room is (8*2)

                                         = 16 dm

The height of the room is (8/2)

                                        = 4 dm.