if V is the volume of the cuboid and x,y,z is the area of the adjacent forces of the cuboid - Maths - Surface Areas and Volumes

Question

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

Jalaj Juneja · Accepted Answer

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
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/editlive_temp/189%20png">
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
∴ l2 b2
h2 = x y z (4)
Volume of the cuboid = l × b ×
h
∴ V = l b h
Squaring on both sides, we get
V 2 = l2
b2 h2
∴ V 2 = xyz (Using(4))
reagards

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.