More Cylinder Problems, 11

Category: Solid Geometry

"Published in Vacaville, California, USA"

A cylinder whose base is a circle is circumscribed about a right prism of altitude 12.6 ft. Find the volume of the cylinder if the base of the prism is an equilateral triangle of side 4 ft. 

Solution:

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

Photo by Math Principles in Everyday LIfe

Consider the base of a cylinder which is a circle that circumscribed about an equilateral triangle as follows 

Photo by Math Principles in Everyday Life

The radius of a circle is equal to two thirds of the altitude of an equilateral triangle. By Pythagorean Theorem, the altitude of an equilateral triangle is

Hence, the radius of a circle is

Therefore, the volume of a circular cylinder is  

But

Hence, the above equation becomes

                         or

 

More Cylinder Problems, 10

Category: Solid Geometry

"Published in Vacaville, California, USA"

A cylinder whose base is a circle is circumscribed about a right prism of altitude 12.6 ft. Find the volume of the cylinder if the base of the prism is a rectangle 3 ft. by 4ft. 

Solution: 

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

Photo by Math Principles in Everyday Life

Consider the base of a cylinder which is a circle that circumscribed about a rectangle as follows

Photo by Math Principles in Everyday Life

The length of the diagonal of a rectangle is equal to the diameter of a circle. By Pythagorean Theorem, the diameter of a circle is

Therefore, the volume of a circular cylinder is 

But

Hence, the above equation becomes

                          or

 

 

 

More Cylinder Problems, 9

Category: Solid Geometry

"Published in Newark, California, USA"

A cylinder whose base is a circle is circumscribed about a right prism of altitude 12.6 ft. Find the volume of the cylinder if the base of the prism is a square of edge 3 ft. 

Solution:

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

Photo by Math Principles in Everyday Life

Consider the base of a cylinder which is a circle that circumscribed about a square as follows

Photo by Math Principles in Everyday Life

The length of the diagonal of a square is equal to the diameter of a circle. By Pythagorean Theorem, the diameter of a circle is

Therefore, the volume of a circular cylinder is

But
 

Hence, the above equation becomes
 

 

 

or