Right Circular Cylinder Problems, 7

Category: Solid Geometry

"Published in Newark, California, USA"

A gas company erected a new gasholder. The gasholder (top and sides) was given three coats of paint. It took 50 bbl. of paint of 50 gal. each to complete the work. The height of the tank was 160 ft. and the diameter of the base was 218 ft. If the paint cost $1.00 per gallon, what was the cost per square yard of surface?

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 calculate the total cost of paint used to paint the top and sides of a gasholder as follows

The total area of the gasholder to be painted is

Therefore, the cost per square yard of a paint required to paint a gasholder is

                             or 

Right Circular Cylinder Problems, 6

Category: Solid Geometry

"Published in Newark, California, USA"

A certain factory manufactures tin cans. It received an order for 10,000 cylindrical tin cans of height 5 in. and diameter 3 in. How many square feet of tin did this order require if 7 sq. in. are allowed for waste and seams in each can?

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 of a cylindrical tin can is

 

 

 

The surface area of a cylindrical tin can is
 

 

 

The area of the excess tin used for waste and seams of a tin can is
 

 

 

Therefore, the total amount of tin used to manufacture 10,000 tin cans is
 

 

Right Circular Cylinder Problems, 5

Category: Solid Geometry

"Published in Vacaville, California, USA"

If a lead pipe ¼ in. thick has an inner diameter of 1½ in., find the number of cubic inches of lead in a piece of pipe 10 ft. long.

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

The first thing that we need to do is to get the area of the cross section which is the section between the two concentric circles as follows

Therefore, the amount of lead in a piece of lead pipe which is the volume of a circular cylinder is