Right Circular Cylinder Problems, 10

Category: Solid Geometry

"Published in Vacaville, California, USA"

A cylindrical standpipe is to contain 343,000 gal. of water. If its height is to be twice its diameter, what must be its dimensions?

Solution:

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

Photo by Math Principles in Everyday Life

Since the given volume of water is in gallons, then we have to convert it first into cubic feet as follows

   

Hence, the diameter of a cylindrical standpipe is

and its height is

Therefore, the dimensions of a cylindrical standpipe are d = 30.791030 ft. and h = 61.58206 ft.

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