Right Circular Cylinder Problems, 9

Category: Solid Geometry

"Published in Newark, California, USA"

A log with a circular cross section is 15 ft. long and 27 in. in diameter at the smaller end. Find the dimensions of the largest piece of timber of length 15 ft. with a uniform square cross section , that can be cut from the log.

Solution:

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

Photo by Math Principles in Everyday Life

In this problem, we will cut the log in order to get the largest piece of timber of the same length which is 15 ft. and the cross section is a square. Now, let's consider the cross section of a log after it is cut as follows

Photo by Math Principles in Everyday Life

The diameter of a log is the hypotenuse of a cross section which is a square that passes through its center. By Pythagorean Theorem, the length of the sides of a square is

                         or

Therefore, the dimensions of a largest timber that can be cut from the log is  

Right Circular Cylinder Problems, 8

Category: Solid Geometry

"Published in Newark, California, USA"

A circular oak table top is 4 ft. in diameter and ¾ in. thick. How heavy is it if oak weighs 47 lb. per cu. ft.?

Solution:

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

Photo by Math Principles in Everyday Life

The volume of a circular oak table top which is the volume of a right circular cylinder is
 

 

 

 

Therefore, the weight of a circular oak table top is
 

 

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