distance question using pi

Question

meg pounded a stake into the ground. when she attached a leash to both the stake and her dog's collar, the dog could reach 9 feet from the stake in any direction. using 3.14 for pi, what is the approximate area of the lawn, in square feet, the dog could reach from the stake?

Answer 1

To answer the question, we need to know the shape of the furthest part of the lawn the dog can cover.  The dog can, at maximum, be 9 feet away from the stake holding its leash in place. 

 

This is a circle, with the center at the stake.  The definition of a circle is all points the same distance away from a given point (the center of the circle).  Since the dog can, at most, be 9 feet (the same distance) from the stake (the center), the area it can cover is a circle.

 

To find the area, we use the formula A = pi*r^2, where A is area of the circle, and r is the radius.  The radius is the distance from the center of the circle to any point on the circle.  In this case, it is 9 feet.  So the answer is

 

A = 3.14 * 81 square feet (ft^2).