The city council has approved the construction of a circular pool in front of the city hall.

Question

The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?

Answer 1

This problem presents maximum ("as large as possible") and minimum ("at least").

 

The pool is a circle and the available space is a rectangle.  The maximum circle is to be placed inside the rectangle.  The smaller dimension of the rectangle (12 feet) limits what can be used.  In fact, the available area might just as well be 12 ft by 12 ft.

 

There must be "at least 2 feet" between the edge of the circle and the brick wall.  This makes the allowable area 8 ft wide (12-2-2).  This is the maximum diameter of the pool.  To solve the problem, we say that the radius of the pool should be 4 feet.