Rectangular Parallelepiped Problem, 9

Category: Solid Geometry

"Published in Newark, California, USA"

An electric refrigerator is built in the form of a rectangular parallelepiped. The inside dimensions are 3 ft. by 2.6 ft. by 1.8 ft. A freezing unit (1.1 ft. by 0.8 ft. by 0.7 ft.) subtracts from the storage room of the box. Find the capacity of the refrigerator. 

Solution:

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

Photo by Math Principles in Everyday Life

There are two rectangular parallelepiped in the figure, the storage room and the freezing unit of a refrigerator. The cooling unit of a refrigerator is equal to the difference of two rectangular parallelepiped. 

For the storage room of a refrigerator, the volume of a rectangular parallelepiped is

 

 
For the freezing unit of a refrigerator, the volume of a rectangular parallelepiped is
 

 

 

 
Therefore, the volume or the capacity of the cooling unit of the refrigerator is
 

 

 

Rectangular Parallelepiped Problem, 8

Category: Solid Geometry, Physics

"Published in Newark, California, USA"

A tank, open at the top, is made of sheet iron 1 in. thick. The internal dimensions of the tank are 4 ft. 8 in. long; 3 ft. 6 in. wide; 4 ft. 4 in. deep. Find the weight of the tank when empty, and find the weight when full of salt water. (Salt water weighs 64 lb. per cu. ft., and iron is 7.2 times as heavy as salt water).

Solution:

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

Photo by Math Principles in Everyday Life

There are two rectangular parallelepiped in the figure, the outside dimensions and the inside dimensions. The volume of a tank that is made of sheet iron 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 which is also the volume of a salt water is

Hence, the volume of a tank is

Therefore, the weight of the empty tank is

The weight of the salt water is

Therefore, the weight of a tank filled with salt water is

 

Rectangular Parallelepiped Problem, 7

Category: Solid Geometry

"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

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