Trapezoid Prism Problems, 2

Category: Solid Geometry

"Published in Newark, California, USA"

A contractor agrees to build a dam, 180 ft. long and 20 ft. high, 12 ft. wide at the bottom and 8 ft. wide at the top, for $9.75 a cubic yard. Find his profit if his costs were $10,000.

Solution:

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

Photo by Math Principles in Everyday Life

The area of the base which is a trapezoid is

The volume of a dam which is a trapezoid prism is

The volume of a dam in cubic yards is

The labor cost of building a dam is

Therefore, the contractor's profit in building a dam is

Trapezoid Prism Problems, 4

Category: Solid Geometry

"Published in Newark, California, USA"

A dam 100 ft. long has a cross section which is a trapezoid whose altitude is 16 ft., and whose upper base is 5 ft. If the lower base angles of the cross section are 50° and 65°, find the volume of material the dam contains.

Solution:

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

Photo by Math Principles in Everyday Life

Since the length of the lower base is not given, then we have to isolate the base first and then label further so that we can solve for its length.

Photo by Math Principles in Everyday Life

Consider the 50° right triangle,

 
Consider the 65° right triangle,

The length of the lower base of a trapezoid which is the cross section of a dam is

 

 

Hence, the area of the base is

Therefore, the volume of a trapezoid prism which is a dam is

Trapezoid Prism Problem, 6

Category: Solid Geometry

"Published in Vacaville, California, USA"

A dam is 40 ft. long, 12 ft. high, 7 ft. wide at the bottom, and 4 ft. wide at the top. How many cubic yards of material were used in constructing it?

Solution:

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

Photo by Math Principles in Everyday Life

The area of the base which is the area of the cross section of a trapezoid prism is 

Therefore, the amount of material used in constructing  a dam which is the volume of trapezoid prism is

                           or