The area of $3$ adjacent surface of a cuboid of value $v$ and $x, y, z$ respectively. Prove that $v^{2} = x y z$ .

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Solution

We have,

Let the cuboid side

$L e n g t h = l$

$B r e a d t h = b$

$H e i g h t = h$

Given that,

The area of 3 adjacent surface of a cuboid of value $v$ and $x, y, z$ respectively.

Prove that:- $v^{2} = x y z$

Proof:-

We know that,

$x = l \times b$

$y = b \times h$

$z = l \times h$

Now,

$x y z = l^{2} b^{2} h^{2} = {(l b h)}^{2}$

$x y z = v^{2} ∴ v = l b h$

Hence, proved.

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