On a water ride at the amusement park, a rotating valve sprays water for 15 ft in all directions. What its the area of the circular wet patch it creates?

The area is 3.14*r^2

The rotating valve would be in the center of the circular wet patch so if it's spraying in all directions, then 15 ft = radius.

Now plug it in.

3.14 x (15) ^2 = 706.5 ft^2