Right Circular Cylinder Problems, 4

Category: Solid Geometry

"Published in Newark, California, USA"

A cubic foot of water weighs about 62.4 lb. What must be the diameter of a cylindrical pail 1 ft. high in order for it to hold the water from 25 lb. of ice? How many square inches of sheet tin are required to make the pan? (Neglect waste in cutting and lapping.)

Solution:

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

Photo by Math Principles in Everyday Life

Since the weight of water or ice as well as its density are given, then we can get the volume of water or ice as follows

The volume of water or ice is the same as the volume of a cylindrical pail. Therefore, the diameter of a cylindrical pail is

                        or

 

The total amount of tin sheet required to make a cylindrical pan is

Right Circular Cylinder Problems, 3

Category: Solid Geometry

"Published in Newark, California, USA"

Find the amount of waste in making the largest possible cylindrical rod from a bar of iron 3 ft. long which has a square cross section whose diagonal is 6 in.

Photo by Math Principles in Everyday Life

Solution:

To analyze the given word problem, let's label further the given figure as follows

Photo by Math Principles in Everyday Life

The first that we need to do is to solve for the area of the cross section of the waste material. The cross section of the waste material is the difference of a square and a circle. 

By using Pythagorean Theorem, the length of one side of a square which is also the diameter of a circle is

Hence, the area of the cross section of the waste material is

 

 

 

 

 

 

 

Therefore, the amount of waste material removed from a bar of iron which is the difference of the volume of a square prism and a right circular cylinder is
 

 

 

                       or

 

 

Right Circular Cylinder Problems, 2

Category: Solid Geometry

"Published in Newark, California, USA"

A paint manufacturer desires a cylindrical steel drum to hold 50 gal. of roof paint. For convenience in handling, it is found necessary to limit the inside diameter to 2½ ft. Find the height of the drum desired. (1 gal. = 231cu. in.)

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 convert the given volume which is the amount of paint inside the cylindrical drum in cubic feet as follows

 

Therefore, the height of the drum desired to hold 50 gal. of roof paint is