Question

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 128 m³. The breadth of the wall is
(a) 30 cm
(b) 40 cm
(c) 22.5 cm
(d) 25 cm

Answer 1

Note : It should be 128 m³ instead of 12.8 m³

(b) 40 cm
Let the breadth of the wall be x cm.
Then, its height = 5x cm
and its length$=\left(8\times 5x\right)\text{cm}$
= 40x cm
Hence, the volume of the wall$=\left(40x\times x\times 5x\right){\text{cm}}^3$
It is given that the volume of the wall = 128 m³.
Therefore,

$$\begin{gathered} \Rightarrow 40x\times x\times 5x=128\times 100\times 100\times 100 \\ \Rightarrow 200x^3=128000000 \\ \Rightarrow x^3=640000 \end{gathered}$$

$$\begin{gathered} \Rightarrow x^3=\left(40\times 40\times 40\right) \\ \Rightarrow x=40\text{cm} \end{gathered}$$