Question

$\mathrm{The}\mathrm{volume}\mathrm{of}a\mathrm{wall},5\mathrm{times}\mathrm{as}\mathrm{high}\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{wide}\mathrm{and}8\mathrm{times}\mathrm{as}\mathrm{long}\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{high},\mathrm{is}12.8\mathrm{cu}.\mathrm{meters}.\mathrm{Find}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{wall}\mathrm{in}\mathrm{cm}.$

• A. 40

Answer 1

The correct option is A 40
Let the breadth of the wall be $x\text{units}$.
Given, height is 5 times the breadth and length is 8 times the height.
Then,
$\text{height}=5\times \text{breadth}=5x\text{units}$
$\text{length}=8\times \text{height}=8\left(5x\right)=40x\text{units}$
We know that,
volume of cuboid = length × breadth × height
Given, volume of cuboid = 12.8 m${}^3$
$\Rightarrow x\times 5x\times 40x=12.8\Rightarrow 200x^3=12.8\Rightarrow x^3=\frac{12.8}{200}=\frac{128}{2000}=\frac{64}{1000}\Rightarrow x^3=\frac{4\times 4\times 4}{10\times 10\times 10}\Rightarrow x=\frac{4}{10}m=\frac{4}{10}\times 100cm=40cm$
$\therefore$ The breadth of the wall = 40 cm