Rectangular Parallelepiped Problem, 11

Category: Solid Geometry, Plane Geometry

"Published in Vacaville, California, USA"

If a, b, and c are the sides of a rectangular parallelepiped, find the length of its diagonal.

Solution:

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

Photo by Math Principles in Everyday Life

The first thing that we need to do is to consider the lower base of the above figure first and then solve for the length of the diagonal by using Pythagorean Theorem.

Photo by Math Principles in Everyday Life

By Pythagorean Theorem, the length of a diagonal of the lower base is

Since all sides as well as the faces of a rectangular parallelepiped are perpendicular to each other, then it follows that x is perpendicular to c. 

Photo by Math Principles in Everyday Life

Therefore, by Pythagorean Theorem, the length of a diagonal of a rectangular parallelepiped is

The diagonal of a rectangular parallelepiped is a length or a distance between the opposite vertices. You can draw four diagonals in a rectangular parallelepiped.

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

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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