Question

The breadth of a room is twice its height, one half of its length and the volume of the room is $512d{m}^3.$ Find its dimensions

Answer 1

Let breadth of a room $\left(b\right)=x$

Then height $\left(h\right)=\frac{x}{2}$

and length $\left(l\right)=2x$

Now, Volume of the room $=length\times breadth\times height=2x\times x\times \frac{x}{2}=x^3$

Volume of the room is given as $512d{m}^3$.

$\Rightarrow x^3=512$

$\Rightarrow x^3=8^3$

$\Rightarrow x=8$

$\therefore$ Length $=2x=2\times 8=16dm$

Breadth $=x=8dm$

and height $=\frac{x}{2}=\frac{8}{2}=4dm$