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Monday, June 9, 2014

Rectangular Parallelepiped Problem, 5

Category: Solid Geometry

"Published in Newark, California, USA"

Building bricks are closely stacked in a pile 7 ft. high, 36 ft. long, and 12 ft. wide. If the bricks are 2 in. by 4 in. by 9 in., how many bricks are in the pile?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Let n = be the number of bricks in a pile
     V1 = be the volume of a brick
     V2 = be the volume of a pile of bricks

The volume of a brick is equal to


   
The volume of a pile of bricks is equal to
 


In cubic inches, the volume of a pile of bricks is





Therefore, the number of bricks in a pile is