Rectangular Parallelepiped Problem, 10

Category: Solid Geometry

"Published in Vacaville, California, USA"

A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 in., a rise of 7 in., and a length of ft.; the landing is 6 ft. by 7 ft. How much material was used in its construction?

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

The first that we need to do is to divide the given figure into rectangular parallelepiped as follows

Photo by Math Principles in Everyday Life

There are one large rectangular parallelepiped and 6 small rectangular parallelepiped in the given figure. Let's assume that the steps of a ladder have 6 small rectangular parallelepiped whose dimensions are all congruent to each other. 

For the large rectangular parallelepiped which is the landing, the volume is

For the small rectangular parallelepiped which is the step of a ladder, the volume is

Therefore, the volume of a ladder which is the amount of a material used in its construction is equal to

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