To pack a set of books, Gautam got cartons of a certain height that were 48 inches long and 27 inches wide. If the volume of such a carton was 22.5 cubic feet, what was the height of each carton? [Use 1 foot = 12 inches.]

30 inches

We know that,

Volume of Cuboid = Length × Breadth × Height 

Given,

Cartons having length = 48 inches

breadth = 27 inches 

The volume of cartoon = 22.5 cubic feet.

Here,

Volume of carton = volume of cuboid

= volume of carton = 48 × 27 × Height

= 22.5 cubic feet = 22.5 × 12 × 12 ×12     (1 foot = 12 inches)

= 22.5 × 12 × 12 × 12 = 48 × 27 × Height     

= 38880 = 1296 × Height 

= Height = 30 inches.