The area of 3 adjacent faces of cuboid are x,y and z . If the volume is V , Prove that V^2 = xyz ???

No

To prove that V^2 = xyz, we need to use the formula for the volume of a cuboid and the areas of its faces. Let's break it down step by step:

Step 1: Start with the formula for the volume of a cuboid.
The volume (V) of a cuboid is given by V = length * width * height.

Step 2: Express the areas of the three adjacent faces of the cuboid.
Let the three adjacent faces have areas x, y, and z, respectively.

The face with area x is equal to length * width.
The face with area y is equal to length * height.
The face with area z is equal to width * height.

Step 3: Express V^2 using the expression for volume from Step 1.
V^2 = (length * width * height)^2

Step 4: Substitute the expressions for faces x, y, and z from Step 2 into the expression for V^2 from Step 3.
V^2 = (length * width * height)^2
= (x * y * z)^2

Step 5: Simplify (x * y * z)^2.
(x * y * z)^2 = x^2 * y^2 * z^2

Therefore, we have proved that V^2 = xyz.

if the dimensions of the brick are a,b,c, then

x = ab
y = ac
z = bc

v^2 = (abc)^2 = a^2b^2c^2 = (ab)(ac)(bc) = xyz