Concentric Circles Problems

Category: Plane Geometry

"Published in Newark, California, USA"

A metal washer 1 in. in diameter is pierced by a ½ in hole. What is the area of one face of the washer?

Solution:

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

Photo by Math Principles in Everyday Life

A metal washer is made from two concentric circles and its a ring shape. 

Let d₁ = be the diameter of outer circle
      d₂ = be the diameter of inner circle
      A₁ = be the area of large circle
      A₂ = be the area of small circle
 
Area of Large Circle:
 

 

 

 
Area of Small Circle:
 

 

 

 

 
Therefore, the area of a metal washer is
 

 

 

 

 

or

 

 

Square, Rectangle, Parallelogram Problems, 8

Category: Plane Geometry

"Published in Vacaville, California, USA"

The official distance between home plate and second base in a baseball diamond is 120 ft. Find the area of the official ball diamond and the distances between the bases. (The official ball diamond is in the form of a square.)

Solution:

To illustrate the problem, it is better to post and label the picture as follows

Photo by Math Principles in Everyday Life

In this problem, the diagonal of a square is given which is a distance between the home plate and the second base. Since the official ball diamond is a square, then the diagonal bisects the square of side x into two equal isosceles right triangles.

Let x = be the distances between the bases
      d = be the distance between home plate and 2nd base
      A = be the area of official ball diamond 

Apply Pythagorean Theorem in order to solve for the distances between the bases as follows

or

Finally, the area of official ball diamond is

Square, Rectangle, Parallelogram Problems, 7

Category: Plane Geometry

"Published in Vacaville, California, USA"

A garden plot is to contain 200 sq. ft. If its length is to be twice its width, what should its dimension be?

Solution:

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

Photo by Math Principles in Everyday Life

The area of a garden lot which is a rectangle is given by the formula

Let x be the width of a rectangle and 2x be the length of a rectangle. If the area of a garden lot is 200 ft² and the length is twice its width, then the above equation becomes

Therefore,