Question

If a cuboid with height $\left(4y\right)\text{cm}$ and breadth $\left(2x\right)\text{cm}$ has the volume equal to $8x^3{y}^3{\text{cm}}^3$, then the length of the cuboid. is:

• A. $x^2{y}^2$
• B. $x{y}^2$
• C. $x^{2}y$
• D. $xy$

Answer 1

The correct option is A $x^2{y}^2$

Given, the height of the cuboid$\left(h\right)=4y\text{cm},$
the breadth of the cuboid$\left(w\right)=2x\text{cm}$
and the volume of the cuboid$\left(V\right)=8x^3{y}^3{\text{cm}}^3$

Let, the length of the cuboid is $l\text{cm}.$

We know that,
$V=l\times w\times h$
$\Rightarrow 8x^3{y}^3=l\times 2x\times 4y$

Simplify R.H.S. of the equation
$\Rightarrow 8x^3{y}^3=l\times (2\times 4)\times (x\times y)$
$\Rightarrow 8x^3{y}^3=l\times 8xy$

Divide both sides by $8xy$
$\Rightarrow \frac{8x^3{y}^3}{8xy}=\frac{l\times 8xy}{8xy}$
$\Rightarrow \frac{8}{8}\times \frac{x^3}{x}\times \frac{y^3}{y}=l$
$\Rightarrow 1\times x^2\times y^2=l$
$\Rightarrow l=x^2{y}^2$