Answer: See the explanation for which answer you need, with and without pi.
Explanation:
Knowing that the sprinkler covers a diameter of 12, let's divide this in half and get the radius, which is 6 feet.
Next, the arc is 195 degrees, so the area of the arc is the following:
A = (θ/360°) × πr^2
A = (195/360) × π(36)
Note that 36 is radius squared, which 6 squared is 36.
195/360 simplifies to 13/24
Multiply the given function and here are two answers:
- With pi in it's symbolic form, it is 19.5π feet squared.
- With pi as a decimal, it is estimated 61.26 feet squared.