# if V is the volume of the cuboid and x,y,z is the area of the adjacent forces of the cuboid than prove that V^2 =xyz.

Dear Student!

Let the length, breath and height of the cuboid be *l *units*,* *b* units and *h* units respectively.

Given, area of three adjacent faces of the cuboid are *x*, *y* and *z* square units.

Area of the face ABEF = *l* × *b* = *x* ...(1)

Area of the face ABCD = *l* × *h* = *y* ...(2)

Area of the face ADGF = *b* × *h* = *z* ...(3)

Multiplying (1), (2) and (3), we get

(*l* × *b*) × (*l* × *h*) × (*b* × *h*) = *x *× *y *× *z*

∴ *l*^{2 }*b*^{2 }*h*^{2} = *x y z* ...(4)

Volume of the cuboid = *l* × *b *× *h*

∴ *V* = *l b h*

Squaring on both sides, we get

*V *^{2} = *l*^{2 }*b*^{2 }*h*^{2}

∴ *V *^{2} = *xyz *(Using(4))

reagards.

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