Right Circular Cylinder Problems

Category: Solid Geometry

"Published in Newark, California, USA"

The diameter of a well is 6 ft., and the water is 7 ft. deep. How many gallons of water are there in the well, reckoning 7.48 gal. to the cubic foot?

Solution:

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

Photo by Math Principles in Everyday Life

Since the diameter of a well as well as the depth of water inside the well are given, then we can calculate the volume of water as follows

Therefore, the amount of water inside the well in gallons is

Circular Cylinder Problems, 7

Category: Solid Geometry

"Published in Newark, California, USA"

 An air duct in the form of a circular cylinder has a cross section of diameter 16 in. The distance between the bases is 20 ft., and the elements are inclined at an angle of 50° to the bases. Find the amount of magnesia required to protect the duct with a magnesia covering ½ in. thick.

Solution: 

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

Photo by Math Principles in Everyday Life

Since the distance of the two bases which is the altitude and the angle of inclination of the elements with respect to the bases are given, then we can solve for the length of element which is the length of an air duct by using sine function as follows

The area of a cross section of an air duct is

Therefore, the amount of magnesia required to protect the air duct which is the volume of a circular cylinder is

Circular Cylinder Problems, 6

Category: Solid Geometry

"Published in Newark, California, USA"

Two vertical brine tanks, with tops on the same level, one 16 ft. deep, the other 4ft. deep, have their tops and bottoms connected by pipes 2 in. in diameter. If the pipe connecting the tops measures 5 ft., find the weight of brine in the other pipe when entirely full. (The brine weighs 66.8 lb. per cu. ft.)

Photo by Math Principles in Everyday Life

Solution:

To analyze more the problem, it is better to label further the given figure as follows

Photo by Math Principles in Everyday Life

By Pythagorean Theorem, the length of a pipe that connects the bottom of two tanks is

 

 

 

 

Hence, the volume of a brine in a pipe that connects the bottom of two tanks is
 

 

 

 

 

 

Therefore, the weight of a brine in a pipe that connects the bottom of two tanks is