Trapezoid Prism Problems, 5

Category: Solid Geometry

"Published in Vacaville, California, USA"

A trench is 200 ft. long and 12 ft. deep, 8 ft. wide at the top and 4 ft. wide at the bottom. How many cubic yards of earth have been recovered?

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 volume of earth removed from a trench which is the volume of trapezoid prism is

                          or

Right Circular Cylinder Problems, 15

Category: Solid Geometry

"Published in Newark, California, USA"

Find the volume of the largest right circular cylinder that can be circumscribed about a rectangular parallelepiped of dimensions 2 ft. by 3 ft. by 4 ft.

Solution:

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

Photo by Math Principles in Everyday Life

There are three ways in finding the volume of a right circular cylinder that circumscribed about a rectangular parallelepiped but we have to choose the largest volume.

If a = 2 ft., b = 3 ft., and c = 4 ft., then the volume of a right circular cylinder is

 

 

 

 

 

If a = 3 ft., b = 2 ft., and c = 4 ft., then the volume of a right circular cylinder is

If a = 2 ft., b = 4 ft., and c = 3 ft., then the volume of a right circular cylinder is

Therefore, the volume of the largest right circular cylinder that can be circumscribed about a rectangular parallelepiped is .