Question

If the areas of three adjacent faces of a cuboid are X,Y and Z respectively,then find the volume of the cuboid.

Answer 1

Explanation:

lb = X

bh = Y

lh = Y

lb × bh × lh = XYZ

l²b²h² = XYZ

(lbh)² = XYZ

lbh = √XYZ

Therefore volume of cuboid = lbh = √XYZ

Answer 2

Explanation:

- 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