Final answer:
The sprinkler will water approximately 8.04 square meters of surface area.
Step-by-step explanation:
The surface area that a sprinkler will water can be found using the formula for the surface area of a circle. The formula is πr^2, where π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The radius of the circular pattern sprayed by the sprinkler is half of the diameter, which is 3.2 meters divided by 2. So, the radius is 1.6 meters.
Now, plug this radius value into the formula:
Surface area = π(1.6)^2 = 3.14(2.56) = 8.04 square meters
Therefore, the sprinkler will water approximately 8.04 square meters of surface area.