Question

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 1

Volume of room = 512 cu. dm
Let height of the room (h) = x
Then breadth (b) = 2x
and length (l) = 2x $\times$ 2 = 4x.
$\therefore$ Volume = $l\times b\times h=4x\times 2x\times x=8x^3$
$\therefore 8x^3=512\Rightarrow x^3=\frac{512}{8}=646=(4{)}^3$
$\therefore$ x=4
$\therefore$ Length = 4x=4 $\times$ 44 = 16 dm
Breadth = 2x = 2 $\times$ 4 = 8 dm
and height = x=4 dm