Right Circular Cylinder Problems, 17

Category: Solid Geometry

"Published in Newark, California, USA"

A cylindrical tin can holding 2 gal. has its height equal to the diameter of its base. Another cylindrical tin can with the same capacity has its height equal to twice the diameter of its base. Find the ratio of the amount of tin required for making the two cans with covers.

Solution:

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

Photo by Math Principles in Everyday Life

The volume of a tin can in cubic inches is

If the height of a tin can equals its diameter, then the diameter is

Hence, the total area of a tin can is

If the height of a tin can is twice its diameter, then the diameter is 

Hence, the total area of a tin can is 

Therefore, the ratio of the amount of tin required for making the two cans with covers is 

Rectangular Parallelepiped Problem, 15

Category: Solid Geometry

"Published in Newark, California, USA"

Two rectangular water tanks with tops on the same level are connected by a pipe through their bottoms. The base of one is 6 in. higher than that of the other. Their dimensions are 4 ft. by 5 ft. by 2½ ft. and 4 ft. by 7 ft. by 3 ft., respectively. How deep is the water in the larger tank when the water they contain equals half their combined capacity, if the 2½ ft. and 3 ft. edges are vertical?

Solution:

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

Photo by Math Principles in Everyday Life

The total volume of two empty rectangular water tanks is

If two tanks are filled with water which is equal to one-half of the total volume of two empty tanks, the above figure becomes

Photo by Math Principles in Everyday Life

Therefore, from the figure above, the depth or height of water in the larger tank 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