Question : If the area of three adjacent faces of a cuboid are x, y and z respectively, then find the volume of cuboid.
Doubt by Saumya
Solution :
Let the length of the cuboid = L
Breadth of the cuboid = B
Height of the cuboid = H
ATQ
LB = x (Given)
L = x/B — (1)
BH = y (Given)
B = y/H — (2)
HL = z (Given)
H = z/L — (3)
Multiplying equation (1), (2) and (3)
LBH=(x/B)×(y/H)×(z/L)
LBH=(xyz)/(LBH)
(LBH)²=xyz
LBH=√(xyz)
V=√(xyz)
where V = LBH = Volume of the cuboid.
Hence, the required volume of the cuboid is √(xyz).