Show that the product of the areas of the floor and two adjacent walls

1.	Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.
Answer» Given, Let length of cuboid = l cm Let breadth of cuboid = b cm Let height of cuboid = h cm So, Area of floor = l x b = lb cm² Product of areas of two adjacent walls = (l x h) x (b x h) = lbh² cm⁴ Product of areas of floor and two adjacent walls = lb x lbh² cm⁶ = l²b²h² = (lbh)² cm⁶ = (volume of cuboid)² Proved

Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.

Answer»

Given,

Let length of cuboid = l cm

Let breadth of cuboid = b cm

Let height of cuboid = h cm

So,

Area of floor = l x b = lb cm²

Product of areas of two adjacent walls = (l x h) x (b x h) = lbh² cm⁴

Product of areas of floor and two adjacent walls = lb x lbh² cm⁶

= l²b²h² = (lbh)² cm⁶

= (volume of cuboid)² Proved