# 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. - Mathematics

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.

#### Solution

$\text { Suppose that the breadth of the room = x dm }$

$\text { Since breadth is twice the height, breadth }= 2 \times \text { height }$

$\text { So, height of the room = } \frac{\text { breadth }}{2}=\frac{x}{2}$

$\text { Also, it is given that the breadth is half the length .}$

$\text { So, breadth }= \frac{1}{2} \times \text { length }$

$\text { i . e . , length }= 2 \times \text { breadth } = 2 \times x$

$\text { Since volume of the room = 512 cu dm, we have }$

$\text { Volume of a cuboid = length } \times\text { breadth } \times \text { height }$

$\Rightarrow 512 = 2 \times x \times x \times \frac{x}{2}$

$\Rightarrow 512 = x^3$

$\Rightarrow x = \sqrt[3]{512} = 8 dm$

$\text { Hence, length of the room }= 2 \times x = 2 \times 8 = 16 dm$

$\text { Breadth of the room = x = 8 dm }$

$\text { Height of the the room } = \frac{x}{2}=\frac{8}{2} = 4 dm$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 21 Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)
Exercise 21.4 | Q 6 | Page 30