Question

The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

• A. 40 cm
• B. 30 cm
• C. 20 cm
• D. 10 cm

Answer 1

The correct option is A 40 cm

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