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

 

 

 

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