If the areas of three adjacent faces of a cuboidal box are 120 sq.cm , 72 sq.cm and 60 sq.cm respectively. Then find the volume of the box ?

The correct answer is: Volume of the given cubical box is 720 cm3.

Step-by-step solution:
Let the edges of the given cuboidal box i.e. cuboid be "a" cm, "b" cm and "c" cm respectively.
Now, We are given that area of adjacent faces of the given cuboid are 120 cm2, 72 cm2 and 60 cm2.
We know that faces of a cuboid are rectangle and area of a rectangle = length  breadth
∴ Areas of the adjacent faces of the given cuboid will be-
edge1 edge2, edge2 edge3 and edge1  edge3
i.e. ab, bc and ac
Now, If we multiply the areas of the 3 adjacent faces, we get-
ab bc  ac = 120 72  60
∴ = 5,18,400
∴ (abc)2 = 5,18,400
∴ abc = ................................................... (Taking square root both the sides)
∴ abc = 720 ..................................................... (Equation i)
Now,
Volume of the given cubical box = length breadth height
∴ Volume of the given cubical box = a  b c
∴ Volume of the given cubical box = 720 ..................................................... (From Equation i)

∴ Volume of the given cubical box is 720 .