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

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