Trapezoid Prism Problems, 7

Category: Solid Geometry

"Published in Newark, California, USA"

A corncrib 20 ft. long has a cross section which is represented in the figure. The crib is entirely filled with corn on the ear. How many bushels of corn does it contain, if 2 bu. of corn on the ear are equal to 1 bu. of shelled corn? (Use the approximation, 1 bu = 1 ¼ cu. ft.)

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

The given figure above is a cross section of a corncrib which is a shape of right trapezoid. The area of a cross section is

The volume of a corncrib which is a trapezoid prism is

If a corncrib is filled with corn on the ear, the number of bushels of corn on the ear is

Therefore, the number of bushels of corn is

Right Circular Cylinder Problems, 20

Category: Solid Geometry

"Published in Newark, California, USA"

A piece of lead pipe is 50 ft. long. Its outer radius is 2 in., and it is ¼ in. thick. Into how many spherical bullets ¼ in. in diameter can be melted?

Solution:

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

Photo by Math Principles in Everyday Life

If the thickness of a lead pipe is ¼ in., then the inner radius is

Hence, the volume of a lead pipe is

If a lead pipe is melted and then converted into spherical bullets of diameter ¼ in., the volume of a piece of spherical bullet is

 

 

 

Therefore, the number of spherical bullets in a lead pipe is
 

 

 

Right Circular Cylinder Problems, 19

Category: Solid Geometry

"Published in Newark, California, USA"

How long a wire 0.1 in. in diameter can be drawn from a block of copper 2 in. by 4 in. by 6 in.?

Solution:

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

Photo by Math Principles in Everyday Life

The volume of a block of copper is

   

Therefore, the length of a wire that can be drawn from a block of copper assuming that a wire is a right circular cylinder is equal to

                       or

 

Right Circular Cylinder Problems, 18

Category: Solid Geometry

"Published in Newark, California, USA"

How much wood is wasted in turning out the largest possible cylindrical rod from a stick whose uniform square cross-sectional area is 10 sq. in. and whose length is 5 ft.?

Solution:

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

Photo by Math Principles in Everyday Life

In this problem, the diameter of a circle is not given. Since the area of a cross-section of a stick is given which is a square, then we can solve for the sides of a square which is also a diameter of a circle as follows

Therefore, the amount of wood wasted in turning out the largest possible cylindrical rod from a stick is