Question

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

Answer 1

Let the height of the cuboid be a, breadth be b, length be c
Volume=a.b.c
Squaring both sides
${v}^{2} = { a}^{2} \times {b}^{2} \times {c}^{2}$
And 3 faces will be,
a.b , b.c , a.c
$= { a}^{2} \times {b}^{2} \times {c}^{2} \\ = x \times y \times z$