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