"Published in Newark, California, USA"
How many cubic yards of material are needed for the foundation of a barn 40 ft. by 80 ft., if the foundation is 2 ft. thick and 12 ft. high?
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
There are two rectangular parallelepiped in the figure, the outside dimensions and the inside dimensions. Their height is the same. The volume or the amount of material needed for the foundation of a barn is equal to the difference of the two rectangular parallelepiped.
For the outside dimensions, the volume of a rectangular parallelepiped is
For the inside dimensions, the volume of a rectangular parallelepiped is
Hence, the volume or the amount of material needed for the foundation of a barn is
Therefore, the volume in cubic yards is equal to
