Answer:
[tex]56.55\ ft^2[/tex]
Step-by-step explanation:
We know that the diameter of the fountain is 3 feet and that it is in the center of the pond.
We know that the area of a circumference is:
[tex]\pi(r)^2[/tex]
where r is the radius of the circumference.
further
d = 2r
Where d is the diameter of the circumference.
Then the radius [tex]r_1[/tex] of the source is 1.5 ft.
The radius [tex]r_2[/tex] of the pond is 1.5 + 3 = 4.5 ft
Finally the area of the pond is equal to the area of the ring that is shown in the image
[tex]A = \pi(r_2)^2 - \pi (r_1)^2\\\\A = \pi(4.5)^2 - \pi(1.5)^2\\\\A = \pi(4.5^2 - 1.5^2)\\\\A = 18\pi = 56.55\ ft^2[/tex]
