Question

please help me to get the answer

Answer 1

Answer:

Step-by-step explanation:

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

follow the fig.

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))

or

Let the sides of the cuboid be a, b and c.

Given x, y and z are areas of three adjacent faces of the cuboid

Hence x=ab,  y=bc, z=ca

(x)(y)(z) = (ab)(bc)(ca)

xyz= (abc)2

abc = √xyz

Thus the volume of cuboid, V= abc = √xyz