The areas of three adjacent faces of a cuboid are $x, y$ and $z$. If the volume is $V$, prove that $V^2 = xyz$.

Given:

The areas of three adjacent faces of a cuboid are $x, y$ and $z$.

The volume is $V$.

To do:

We have to prove that $V^2 = xyz$.

Solution:

Let $a, b$ and $c$ be the dimensions of a cuboid.

This implies,

$x = ab, y = bc, z = ca$

This implies,

$V = abc$

LHS. $= V^2$

$= (abc)^2$

$= a^2b^2c^2$

$= ab.bc.ca$

$= xyz$

$=$ RHS

Hence proved.

Tutorialspoint

Updated on: 10-Oct-2022

16 Views

Kickstart Your Career

Get certified by completing the course

Get Started