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.

Given:

The breadth of a room is twice its height, one half of its length and the volume of the room is $512$ cu. dm.

To do:

We have to find its dimensions.

Solution:

Let the breadth of the room be $(b) = x$

This implies,

Height of the room $(h)=\frac{x}{2}$

Length of the room $(l)=2 x$

Therefore,

Volume of the room $=l b h$

$=x \times \frac{x}{2} \times 2 x$

$=x^{3}$

$x^{3}=512$

$=(8)^{3}$

$\Rightarrow x=8$

This implies,

Length $=2 x$

$=2 \times 8$

$=16 \mathrm{dm}$

Breadth $=x$

$=8 \mathrm{dm}$

Height $=\frac{x}{2}$

$=\frac{8}{2}$

$=4 \mathrm{dm}$

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Updated on: 10-Oct-2022

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